The b-symbol weight distribution of irreducible cyclic codes and related consequences

03/22/2022

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by   Hongwei Zhu, et al.

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The b-symbol read channel is motivated by the limitations of the reading process in high density data storage systems. The corresponding new metric is a generalization of the Hamming metric known as the b-symbol weight metric and has become an important object in coding theory. In this paper, the general b-symbol weight enumerator formula for irreducible cyclic codes is presented by using the Gaussian period and a new invariant #U(b,j,N_1). The related b-symbol weight hierarchies {d_1(),d_2(),…,d_K()} (K=()) are given for some cases. The shortened codes which are optimal from some classes of irreducible cyclic codes are given, where the shorten set 𝒯 is the complementary set of b-symbol support of some codeword with the minimal b-symbol weight.