A class of optimal p-ary codes from one-weight codes over Fp [ u ] / 〈 um 〉

Minjia Shi; Shixin Zhu; Shanlin Yang

doi:10.1016/j.jfranklin.2012.05.014

A class of optimal p-ary codes from one-weight codes over ^Fp [ u ] / 〈 ^um 〉

Minjia Shi
, Shixin Zhu
, Shanlin Yang

Research output: Contribution to journal › Article › peer-review

64 Scopus citations

Abstract

We characterize the structures and properties of one-homogeneous weight linear codes C^k1,...,^km over ^Fp[u]/ 〈^um〉 of type 1^k1p^k2⋯(pm- ¹)^km with one unique nonzero weight w₀. We introduce a distance-preserving Gray map from (^Fp[u] /〈^um〉)ⁿ to Fppm-¹n. By the Gray map, we obtain a class of optimal p-ary one-Hamming weight linear codes from one-homogeneous weight linear codes over ^Fp[u]/〈 ^um〉. We conclude by constructing some one-homogeneous codes over ^Fp[u]/〈^um〉.

Original language	English
Pages (from-to)	929-937
Number of pages	9
Journal	Journal of the Franklin Institute
Volume	350
Issue number	5
DOIs	https://doi.org/10.1016/j.jfranklin.2012.05.014
State	Published - Jun 2013
Externally published	Yes

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10.1016/j.jfranklin.2012.05.014

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title = "A class of optimal p-ary codes from one-weight codes over Fp [ u ] / 〈 um 〉",

abstract = "We characterize the structures and properties of one-homogeneous weight linear codes Ck1,...,km over Fp[u]/ 〈um〉 of type 1k1pk2⋯(pm- 1)km with one unique nonzero weight w0. We introduce a distance-preserving Gray map from (Fp[u] /〈um〉)n to Fppm-1n. By the Gray map, we obtain a class of optimal p-ary one-Hamming weight linear codes from one-homogeneous weight linear codes over Fp[u]/〈 um〉. We conclude by constructing some one-homogeneous codes over Fp[u]/〈um〉.",

author = "Minjia Shi and Shixin Zhu and Shanlin Yang",

year = "2013",

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doi = "10.1016/j.jfranklin.2012.05.014",

language = "英语",

volume = "350",

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journal = "Journal of the Franklin Institute",

issn = "0016-0032",

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TY - JOUR

T1 - A class of optimal p-ary codes from one-weight codes over Fp [ u ] / 〈 um 〉

AU - Shi, Minjia

AU - Zhu, Shixin

AU - Yang, Shanlin

PY - 2013/6

Y1 - 2013/6

N2 - We characterize the structures and properties of one-homogeneous weight linear codes Ck1,...,km over Fp[u]/ 〈um〉 of type 1k1pk2⋯(pm- 1)km with one unique nonzero weight w0. We introduce a distance-preserving Gray map from (Fp[u] /〈um〉)n to Fppm-1n. By the Gray map, we obtain a class of optimal p-ary one-Hamming weight linear codes from one-homogeneous weight linear codes over Fp[u]/〈 um〉. We conclude by constructing some one-homogeneous codes over Fp[u]/〈um〉.

AB - We characterize the structures and properties of one-homogeneous weight linear codes Ck1,...,km over Fp[u]/ 〈um〉 of type 1k1pk2⋯(pm- 1)km with one unique nonzero weight w0. We introduce a distance-preserving Gray map from (Fp[u] /〈um〉)n to Fppm-1n. By the Gray map, we obtain a class of optimal p-ary one-Hamming weight linear codes from one-homogeneous weight linear codes over Fp[u]/〈 um〉. We conclude by constructing some one-homogeneous codes over Fp[u]/〈um〉.

UR - https://www.scopus.com/pages/publications/84876408340

U2 - 10.1016/j.jfranklin.2012.05.014

DO - 10.1016/j.jfranklin.2012.05.014

M3 - 文章

AN - SCOPUS:84876408340

SN - 0016-0032

VL - 350

SP - 929

EP - 937

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 5

ER -

A class of optimal p-ary codes from one-weight codes over ^Fp [ u ] / 〈 ^um 〉

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