Generalized Pair Weights of Linear Codes and Linear Isomorphisms Preserving Pair Weights

Liu, Hongwei; Pan, Xu

doi:10.1109/tit.2021.3120229

Cited by 10 publications

(2 citation statements)

References 24 publications

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“…It is worth mentioning that there are other interesting connections between the two metrics. Liu and Pan [22,30] considered the superposition of two metrics. They call this superposition a generalized b-weight (we prefer to call it a generalized b-symbol weight).…”

Section: Introductionmentioning

confidence: 99%

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

Zhu¹,

Shi²

2022

Preprint

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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 (C), d 2 (C), . . . , d K (C)} (K = dim(C)) 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.

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Section: Introductionmentioning

confidence: 99%

“…They call this superposition a generalized b-weight (we prefer to call it a generalized b-symbol weight). For more details, we refer the readers to [22,30].…”

Section: Introductionmentioning

confidence: 99%