## Book

**R.M. Roth**,

*Introduction to Coding Theory*,

Cambridge University Press, Cambridge, UK, 2006.

## Survey on constrained coding

**B.H. Marcus, R.M. Roth, P.H. Siegel**,

Constrained systems and coding for recording channels,

in*Handbook of Coding Theory*, V.S. Pless and W.C. Huffman (Editors), Elsevier, Amsterdam, 1998, pp. 1635–1764.

A short version of this survey, by the same authors, appeared under the title “Modulation codes for digital data storage,”

in*Different Aspects of Coding Theory*, Proceedings of Symposia in Applied Mathematics, Vol. 50, R.C. Calderbank (Editor), American Mathematical Society, Providence, Rhode Island, 1995, pp. 41–87.

An extended (incomplete) version of the survey is available in a form of Lecture Notes.

## Journal papers

**Reed–Solomon codes and MDS codes****Array codes****Applications of error-correcting codes****Other ECC results****Constrained systems and modulation codes****Spectral-null codes****Multi-dimensional constrained coding****Other results**

### Reed–Solomon codes and MDS codes

**R.M. Roth**,

Higher-order MDS codes,

*IEEE Trans. Inf. Theory*, to appear.**T. Kolan, R.M. Roth**,

Burst list decoding of interleaved Reed–Solomon codes,

*IEEE Trans. Inf. Theory*, 60 (2014), 182–189.**R.M. Roth, P.O. Vontobel**,

List decoding of burst errors,

*IEEE Trans. Inf. Theory*, 55 (2009), 4179–4190.**J. Han, P.H. Siegel, R.M. Roth**,

Single-exclusion number and the stopping redundancy of MDS codes,

*IEEE Trans. Inf. Theory*, 55 (2009), 4155–4166.**R.M. Roth, V. Skachek**,

Improved nearly-MDS expander codes,

*IEEE Trans. Inf. Theory*, 52 (2006), 3650–3661.**E. Louidor, R.M. Roth**,

Lowest density MDS codes over extension alphabets,

*IEEE Trans. Inf. Theory*, 52 (2006), 3186–3197.**G. Ruckenstein, R.M. Roth**,

Bounds on the list-decoding radius of Reed–Solomon codes,

*SIAM J. Disc. Math.*, 17 (2003), 171–195.**R.M. Roth, G. Ruckenstein**,

Efficient decoding of Reed–Solomon codes beyond half the minimum distance,

*IEEE Trans. Inf. Theory*, 46 (2000), 246–257.**M. Blaum, R.M. Roth**,

On lowest density MDS codes,

*IEEE Trans. Inf. Theory*, 45 (1999), 46–59.**R.M. Roth, A. Lempel**,

On MDS codes via Cauchy matrices,

*IEEE Trans. Inf. Theory*, 35 (1989), 1314–1319.**R.M. Roth, A. Lempel**,

A construction of non-Reed–Solomon type MDS codes,

*IEEE Trans. Inform. Theory*, 35 (1989), 655–657.**R.M. Roth, A. Lempel**,

Composition of Reed–Solomon codes and geometric designs,

*IEEE Trans. Inf. Theory*, 34 (1988), 810–816.**G. Seroussi, R.M. Roth**,

On MDS extensions of generalized Reed–Solomon codes,

*IEEE Trans. Inf. Theory*, IT-32 (1986), 349–354.**R.M. Roth, G. Seroussi**,

On cyclic MDS codes of length*q*over GF(*q*),

*IEEE Trans. Inf. Theory*, IT-32 (1986), 284–285.**R.M. Roth, G. Seroussi**,

On generator matrices of MDS codes,

*IEEE Trans. Inf. Theory*, IT-31 (1985), 826–830.

### Array codes

**R.M. Roth**,

On decoding rank-metric codes over large fields,

*IEEE Trans. Inf. Theory*, 64 (2018), 944–951.**R.M. Roth, P.O. Vontobel**,

Coding for combined block-symbol error correction,

*IEEE Trans. Inf. Theory*, 60 (2014), 2697–2713.**R.M. Roth, G. Seroussi**,

Reduced-redundancy product codes for burst error correction,

*IEEE Trans. Inf. Theory*, 44 (1998), 1395–1406.**R.M. Roth**,

Probabilistic crisscross error correction,

*IEEE Trans. Inf. Theory*, 43 (1997), 1425–1438.**R.M. Roth**,

Tensor codes for the rank metric,

*IEEE Trans. Inf. Theory*, 42 (1996), 2146–2157.**M. Blaum, R.M. Roth**,

New array codes for multiple phased burst correction,

*IEEE Trans. Inf. Theory*, 39 (1993), 66–77.**R.M. Roth**,

Maximum-rank array codes and their application to crisscross error correction,

*IEEE Trans. Inf. Theory*, 37 (1991), 328–336 (see correction in 38 (1992), 1183).

### Applications of error-correcting codes

**R.M. Roth**,

Analog error-correcting codes,

*IEEE Trans. Inf. Theory*, 66 (2020), 4075–4088.**R.M. Roth**,

Fault-tolerant dot-product engines,

*IEEE Trans. Inf. Theory*, 65 (2019), 2046–2057.**A. Bremler-Barr, D. Hay, D. Hendler, R.M. Roth**,

PEDS: A Parallel error detection scheme for TCAM devices,

*IEEE/ACM Trans. Netw.*, 18 (2010), 1665–1675.**R.M. Roth, W. Robinett, P.J. Kuekes, R.S. Williams**,

Defect-tolerant demultiplexer circuits based on threshold logic and coding,

*Nanotechnology*, 20 (2009), #135201 (14pp).**P.J. Kuekes, W. Robinett, R.M. Roth, G. Seroussi, G.S. Snider, R.S. Williams**,

Resistor-logic demultiplexers for nanoelectronics based on constant-weight codes,

*Nanotechnology*, 17 (2006), 1052–1061.**E. Petrank, R.M. Roth**,

Is code equivalence easy to decide?,

*IEEE Trans. Inf. Theory*, 43 (1997), 1602–1604.**M. Naor, R.M. Roth**,

Optimal file sharing in distributed networks,

*SIAM J. Comput.*, 24 (1995), 158–183.**R.M. Roth, G.M. Benedek**,

Interpolation and approximation of sparse multivariate polynomials over GF(2),

*SIAM J. Comput.*, 20 (1991), 291–314.

### Other ECC results

**R.M. Roth**,

Asymptotic bounds on the rate of locally repairable codes,

*IEEE Trans. Inf. Theory*, 68 (2022), 1581–1598.**E. Ordentlich, R.M. Roth**,

On the pointwise threshold behavior of the binary erasure polarization subchannels,

*IEEE Trans. Inf. Theory*, 65 (2019), 6044–6055.**R.M. Roth, A. Zeh**,

On spectral design methods for quasi-cyclic codes,

*IEEE Trans. Inf. Theory*, 65 (2019), 2637–2647.**A. Sharov, R.M. Roth**,

On the capacity of generalized Ising channels,

*IEEE Trans. Inf. Theory*, 63 (2017), 2338–2356.**R.M. Roth, A. Zeh**,

Long cyclic codes over GF(4) and GF(8) better than BCH codes in the high-rate region,

*IEEE Trans. Inf. Theory*, 63 (2017), 150–158.**A. Sharov, R.M. Roth**,

New bounds and constructions for granular media coding,

*IEEE Trans. Inf. Theory*, 61 (2015), 4227–4238.**A. Sharov, R.M. Roth**,

Bounds and constructions for granular media coding,

*IEEE Trans. Inf. Theory*, 60 (2014), 2010–2027.**R.M. Roth, G. Seroussi**,

Bounds for binary codes with narrow distance distributions,

*IEEE Trans. Inf. Theory*, 53 (2007), 2760–2768.**R.M. Roth, G. Seroussi**,

Symbol-intersecting codes,

*IEEE Trans. Inf. Theory*, 51 (2005), 2266–2281.**R.M. Roth, G. Seroussi**,

Location-correcting codes,

*IEEE Trans. Inf. Theory*, 42 (1996), 554–565.**N. Alon, J. Bruck, J. Naor, M. Naor, R.M. Roth**,

Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs,

*IEEE Trans. Inf. Theory*, 38 (1992), 509–516.**R.M. Roth, A. Lempel**,

Application of circulant matrices to the construction and decoding of linear codes,

*IEEE Trans. Inf. Theory*, 36 (1990), 1157–1163.**R.M. Roth, G. Seroussi**,

Encoding and decoding of BCH codes using light and short codewords,

*IEEE Trans. Inf. Theory*, 34 (1988), 593–596.

### Constrained systems and modulation codes

**R.M. Roth, Paul H. Siegel**,

Variable-length constrained coding and Kraft conditions: The parity-preserving case,

*IEEE Trans. Inf. Theory*, 67 (2021), 6179–6192.**R.M. Roth, Paul H. Siegel**,

On bi-modal constrained coding,

*IEEE Trans. Inf. Theory*, 67 (2021), 1609–1621.**G. Ruckenstein, R.M. Roth**,

Lower bounds on the anticipation of encoders for input-constrained channels,

*IEEE Trans. Inf. Theory*, 47 (2001), 1796–1812.**J. Hogan, R.M. Roth, G. Ruckenstein**,

Nested block decodable runlength-limited codes,

*IEEE Trans. Inf. Theory*, 47 (2001), 1630–1638.**J. Hogan, R.M. Roth, G. Ruckenstein**,

Nested input-constrained codes,

*IEEE Trans. Inf. Theory*, 46 (2000), 1302–1316.**J.L. Fan, B.H. Marcus, R.M. Roth**,

Lossless sliding-block compression of constrained systems,

*IEEE Trans. Inf. Theory*, 46 (2000), 624–633.**J.J. Ashley, B.H. Marcus, R.M. Roth**,

On the decoding delay of encoders for input-constrained channels,

*IEEE Trans. Inf. Theory*, 42 (1996), 1948–1956.**J.J. Ashley, B.H. Marcus, R.M. Roth**,

Construction of encoders with small decoding look-ahead for input-constrained channels,

*IEEE Trans. Inf. Theory*, 41 (1995), 55–76.**B.H. Marcus, R.M. Roth**,

Improved Gilbert–Varshamov bound for constrained systems,

*IEEE Trans. Inf. Theory*, 38 (1992), 1213–1221.**B.H. Marcus, R.M. Roth**,

Bounds on the number of states in encoder graphs for input-constrained channels,

*IEEE Trans. Inf. Theory*, 37 (1991), 742–758.

### Spectral-null codes

**A. Mazumdar, R.M. Roth, P.O. Vontobel**,

On linear balancing sets,

*Adv. Math. Commun.*, 4 (2010), 345–361.**R.M. Roth**,

On runlength-limited coding with DC control,

*IEEE Trans. Commun.*, 48 (2000), 351–358.**V. Skachek, T. Etzion, R.M. Roth**,

Efficient encoding algorithm for third-order spectral-null codes,

*IEEE Trans. Inf. Theory*, 44 (1998), 846–851.**R.M. Roth**,

Spectral-null codes and null spaces of Hadamard submatrices,

*Des. Codes Cryptogr.*, 9 (1996), 177–191.**R.M. Roth, P.H. Siegel, A. Vardy**,

High-order spectral-null codes: Constructions and bounds,

*IEEE Trans. Inf. Theory*, 40 (1994), 1826–1840.**R.M. Roth, P.H. Siegel**,

Lee-metric BCH codes and their application to constrained and partial-response channels,

*IEEE Trans. Inf. Theory*, 40 (1994), 1083–1096.

### Multi-dimensional constrained coding

**E. Ordentlich, F. Parvaresh, R.M. Roth**,

Asymptotic enumeration of binary matrices with bounded row and column sums,

*SIAM J. Disc. Math.*, 26 (2012), 1550–1575.**E. Ordentlich, R.M. Roth**,

Low complexity two-dimensional weight-constrained codes,

*IEEE Trans. Inf. Theory*, 58 (2012), 3892–3899.**I. Tal, R.M. Roth**,

Convex programming upper bounds on the capacity of 2-D constraints,

*IEEE Trans. Inf. Theory*, 57 (2011), 381–391.**I. Tal, R.M. Roth**,

Bounds on the rate of 2-D bit-stuffing encoders,

*IEEE Trans. Inf. Theory*, 56 (2010), 2561–2567.**A. Sharov, R.M. Roth**,

Two-dimensional constrained coding based on tiling,

*IEEE Trans. Inf. Theory*, 56 (2010), 1800–1807.**I. Tal, T. Etzion, R.M. Roth**,

On row-by-row coding for 2-D constraints,

*IEEE Trans. Inf. Theory*, 55 (2009), 3565–3576.**E. Ordentlich, R.M. Roth**,

Independent sets in regular hypergraphs and multi-dimensional runlength-limited constraints,

*SIAM J. Disc. Math.*, 17 (2004), 615–623.**S. Halevy, J. Chen, R.M. Roth, P.H. Siegel, J.K. Wolf**,

Improved bit-stuffing bounds on two-dimensional constraints,

*IEEE Trans. Inf. Theory*, 50 (2004), 824–838.**S. Halevy, R.M. Roth**,

Parallel constrained coding with application to two-dimensional constraints,

*IEEE Trans. Inf. Theory*, 48 (2002), 1009–1020.**R.M. Roth, P.H. Siegel, J.K. Wolf**,

Efficient coding schemes for the hard-square model,

*IEEE Trans. Inf. Theory*, 47 (2001), 1166–1176.**E. Ordentlich, R.M. Roth**,

Two-dimensional weight-constrained codes through improved enumeration bounds,

*IEEE Trans. Inf. Theory*, 46 (2000), 1292–1301.**R. Talyansky, T. Etzion, R.M. Roth**,

Efficient code constructions for certain two-dimensional constraints,

*IEEE Trans. Inf. Theory*, 45 (1999), 794–799.

### Other results

**R.N. Berman, R.M. Roth**,

On the number of factorizations of polynomials over finite fields,

*J. Comb. Theory Ser. A*, 182 (2021), #105462 (39pp).**R.M. Roth, N. Raviv, I. Tamo**,

Construction of Sidon spaces with applications to coding,

*IEEE Trans. Inf. Theory*, 64 (2018), 4412–4422.**E. Ordentlich, R.M. Roth**,

Two-dimensional maximum-likelihood sequence detection is NP hard,

*IEEE Trans. Inf. Theory*, 57 (2011), 7661–7670**R.M. Roth, K. Viswanathan**,

On the hardness of decoding the Gale–Berlekamp code,

*IEEE Trans. Inf. Theory*, 54 (2008), 1050–1060.**V. Skachek, R.M. Roth**,

Probabilistic algorithm for finding roots of linearized polynomials,

*Des. Codes Cryptogr.*, 46 (2008), 17–23.**N. Merhav, R.M. Roth, E. Arikan**,

Hierarchical guessing with a fidelity criterion,

*IEEE Trans. Inf. Theory*, 45 (1999), 330–337.**R. Bar-Yehuda, D. Geiger, J. Naor, R.M. Roth**,

Approximation algorithms for the vertex feedback set problem with applications to constraint satisfaction and Bayesian inference,

*SIAM J. Comput.*, 27 (1998), 942–959.**J. Naor, R.M. Roth**,

Constructions of permutation arrays for certain scheduling cost measures,

*Random Structures and Algorithms*, 6 (1995), 39–50.**R.M. Roth, A. Lempel**,

*t*-sum generators of finite Abelian groups,

*Discrete Math.*, 103 (1992), 279–292.