# Constacyclic Symbol-Pair Codes: Lower Bounds and Optimal Constructions

@article{Chen2017ConstacyclicSC, title={Constacyclic Symbol-Pair Codes: Lower Bounds and Optimal Constructions}, author={Bocong Chen and Liren Lin and Hongwei Liu}, journal={IEEE Transactions on Information Theory}, year={2017}, volume={63}, pages={7661-7666} }

Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that pair distance cannot be improved for given length and code size. The contribution of this paper is twofold. First, we present three lower bounds for the minimum pair distance of constacyclic codes, the…

## Tables from this paper

## 44 Citations

MDS and AMDS symbol-pair codes are constructed from repeated-root codes

- Computer ScienceArXiv
- 2022

This paper proposes three new classes of MDS symbol-pair codes with the length lp or 3 p and gives two newclasses of (almost maximal distance separable) AM DS symbol- Pair codes with a length of 4 p by virtue of repeated-root cyclic codes.

Constructions of MDS symbol-pair codes with minimum distance seven or eight

- Computer ScienceDesigns, Codes and Cryptography
- 2022

Two new classes of MDS symbol-pair codes with minimum symbol- Pair distance seven or eight are constructed by utilizing repeated-root cyclic codes over Fp, where p is a prime.

A Characterization of MDS Symbol-pair Codes over Two Types of Alphabets

- Computer ScienceArXiv
- 2021

This paper characterize the symbol-pair distances of some constacyclic codes of arbitrary lengths over finite fields and a class of finite chain rings and shows that there is no other MDS symbol- Pair code among the class of constacyClic codes except for what is presented.

MDS symbol-pair codes from repeated-root cyclic codes

- Computer ScienceDes. Codes Cryptogr.
- 2022

Two new classes of MDS symbol-pair codes are proposed by utilizing repeated-root cyclic codes over finite fields with odd characteristic, and it should be noted that these codes have minimum symbol- Pair distance ten or twelve.

New MDS Symbol-Pair Codes from Repeated-Root Cyclic Codes over Finite Fields

- Computer ScienceArXiv
- 2020

Three new classes of MDS symbol-pair codes with minimum symbol- Pair distance seven or eight are proposed by virtue of repeated-root cyclic codes, obtained by determining the solutions of certain equations over finite fields.

New MDS Symbol-Pair Codes From Repeated-Root Codes

- Computer ScienceIEEE Communications Letters
- 2018

Three new MDS symbol-pair codes with minimum pair-distance six or seven through repeated-root constacyclic codes are constructed, in contrast with classical MDS codes, they have relatively large length.

A new class of MDS symbol-pair codes

- Computer ScienceArXiv
- 2021

A class of q-ary MDS symbol-pair codes with dimension k and length n is constructed, where q is a prime power and the symbol- Pair weight distributions for these codes are determined by enumerating the number of polynomials with given roots.

Covering b-Symbol Metric Codes and the Generalized Singleton Bound

- Computer ScienceArXiv
- 2022

It is proved that there is no perfect linear symbol-pair code with the minimum pair distance 7 and there are no perfect b -symbol metric code if b ≥ n +12 and a lot of cyclic and algebraic-geometric codes are proved non-perfect in the b -Symbol metric.

Maximum Distance Separable Codes for b-Symbol Read Channels

- Computer ScienceFinite Fields Their Appl.
- 2018

Construction of Cyclic and Constacyclic Codes for b-symbol Read Channels Meeting the Plotkin-like Bound

- Computer ScienceArXiv
- 2016

This paper shows the Plotkin-like bound of MDS codes for b-symbol read channels and presents a construction on irreducible cyclic codes and constacyclic codes meeting the plotkin- like bound.

## References

SHOWING 1-10 OF 12 REFERENCES

Maximum distance separable symbol-pair codes

- Computer Science2012 IEEE International Symposium on Information Theory Proceedings
- 2012

These codes are maximum distance separable (MDS) in the sense that they meet the Singleton-type bound, and it is shown that q-ary MDS symbol-pair codes can have length Ω(q2).

Maximum Distance Separable Codes for Symbol-Pair Read Channels

- Computer ScienceIEEE Transactions on Information Theory
- 2013

These codes are maximum distance separable (MDS) in the sense that they meet the Singleton-type bound and it is shown that q-ary MDS symbol-pair codes can have length Ω(q2), in contrast to classical codes.

A Construction of New MDS Symbol-Pair Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2015

This paper construct some new MDS symbol-pair codes with minimum pair-distance five and six based on constacyclic codes, and compared with classical q-ary MDS codes, the constructed codes have length up to q2+q+1.

Constructions and Decoding of Cyclic Codes Over $b$ -Symbol Read Channels

- Computer ScienceIEEE Transactions on Information Theory
- 2016

It is shown that, for a given linear cyclic code with a minimum Hamming distance dH, the minimum pair distance is at least dH + (dH/2).

Codes for Symbol-Pair Read Channels

- Computer ScienceIEEE Transactions on Information Theory
- 2011

Asymptotic analysis of pair-error correction shows that there exist pair- error codes with rates that are strictly higher than the best known codes in the Hamming metric.

Symbol-pair codes: Algebraic constructions and asymptotic bounds

- Computer Science2011 IEEE International Symposium on Information Theory Proceedings
- 2011

Asymptotic lower bounds on code rates show that codes for pair-errors provably exist for rates strictly higher than codes for the Hamming metric.

On Repeated-root Cyclic Codes

- Computer ScienceIEEE Trans. Inf. Theory
- 1991

The relative minimum distance d/sub min//n of q-ary repeated-root cyclic codes of rate r>or=R is proven to tend to zero as the largest multiplicity of a root of the generator g(x) increases to infinity.

Constacyclic Codes and Some New Quantum MDS Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2014

This paper constructs some new quantum MDS codes by employing the Hermitian construction, based on classical constacyclic codes, to construct quantum codes that have a large minimum distance.

Application of Constacyclic Codes to Quantum MDS Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2015

Four classes of dual-containing constacyclic MDS codes are constructed and their parameters are computed, and the quantum M DS codes derived from these parameters have minimum distance bigger than the ones available in the literature.

Fundamentals of Error-Correcting Codes

- Computer Science
- 1975

This chapter discusses the development of soft decision and iterative decoding in linear codes, as well as some of the techniques used in convolutional codes.