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arXiv · 1609.09236

Maximum Distance Separable Codes for $b$-Symbol Read Channels

Baokun Ding·Tao Zhang·Gennian Ge
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Abstract

Recently, Yaakobi et al. introduced codes for $b$-symbol read channels, where the read operation is performed as a consecutive sequence of $b>2$ symbols. In this paper, we establish a Singleton-type bound on $b$-symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum $b$-distance. Based on projective geometry and constacyclic codes, we construct new families of linear MDS $b$-symbol codes over finite fields. And in some sense, we completely determine the existence of linear MDS $b$-symbol codes over finite fields for certain parameters.

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Baokun Ding, Tao Zhang, Gennian Ge. 2016-09-29. Maximum Distance Separable Codes for $b$-Symbol Read Channels. https://arxiv.org/abs/1609.09236

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