Details

Autor(en) / Beteiligte

• Chen, Bocong
• Liu, Hongwei

Titel

New Bounds on the Code Size of Symbol-Pair Codes

Ist Teil von

• IEEE transactions on information theory, 2023-02, Vol.69 (2), p.941-950

Ort / Verlag

New York: IEEE

Erscheinungsjahr

2023

Quelle

IEEE Xplore

Beschreibungen/Notizen

• Classical error-correcting codes under the Hamming metric are used to correct substitution and erasure errors. Motivated by the limitations of the reading process in high density data storage systems, a new class of codes called symbol-pair (metric) codes was designed to protect against pair errors in symbol-pair read channels. For a given alphabet of size <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula> and given values of <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula> with <inline-formula> <tex-math notation="LaTeX">1\leq d\leq n </tex-math></inline-formula>, let <inline-formula> <tex-math notation="LaTeX">A_{p}(n,d,q) </tex-math></inline-formula> denote the largest possible code size for which there exists a <inline-formula> <tex-math notation="LaTeX">q </tex-math></inline-formula>-ary code of length <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> with minimum pair-distance at least <inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula>. In this paper, new upper and lower bounds on <inline-formula> <tex-math notation="LaTeX">A_{p}(n,d,q) </tex-math></inline-formula> are presented. Several examples are included to illustrate our main results; some examples are optimal in the sense that they meet the corresponding bounds, and the rest examples are meant to show that our bounds may perform better than some of the previously known ones in certain cases. In addition, we show that any symbol-pair code over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q} </tex-math></inline-formula> can be viewed as a Hamming metric code over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q^{2}} </tex-math></inline-formula> with the same parameters. Consequently, the theory of classical codes over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q^{2}} </tex-math></inline-formula> can be used directly to symbol-pair codes; in particular, by virtue of this result, some known results can be reobtained immediately.