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New constructions of MDS symbol-pair codes via simple-root cyclic codes by Qiu, Rongxing; Fang, Weijun is a scholarly article available to read on EtoBox.

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In modern storage technologies, symbol-pair codes have emerged as a crucial framework for addressing errors in channels where symbols are read in overlapping pairs to guard against pair errors. A symbol-pair code that meets the Singleton-type bound is called a maximum distance separable (MDS) symbol-pair code. MDS symbol-pair codes are optimal in the sense that they have the highest pair error-correcting capability. In this paper, we focus on new constructions of MDS symbol-pair codes using simple-root cyclic codes. Specifically, three new infinite families of $(n, d_P)_q$-MDS symbol-pair codes are obtained: (1) $(n=4q+4,d_P=7)_q$ for $q\equiv 1\pmod 4$; (2) $(n=4q-4,d_P=8)_q$ for $q\equiv 3\pmod 4$; (3) $(n=2q+2,d_P=9)_q$ for $q$ being an odd prime power. The first two constructions are based on analyzing the solutions of certain equations over finite fields. The third construction arises from the decomposition of cyclic codes, where we utilize the orthogonal relationships between component codes and their duals to rigorously exclude the presence of specific codewords. It is worth noting that for the pair distance $d_P=7$ or $8$, our $q$-ary MDS symbol-pair codes achieve the longe

Author

Qiu, Rongxing; Fang, Weijun

Published

2025

Language

EN