Further results on the semilinear equivalence of linear codes

Zihui Liu; Xiangyong Zeng

doi:10.1016/j.ins.2012.09.007

Further results on the semilinear equivalence of linear codes

Zihui Liu^*, Xiangyong Zeng

^*Corresponding author for this work

School of Mathematics and Statistics

Hubei University

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

1 Citation (Scopus)

Abstract

Based on relative subcodes, we address an equivalent condition for a one-to-one semilinear mapping between two linear codes to be in fact a semimonomial transformation, that is, the underlying two codes are semilinearly equivalent. The result in the present paper substantially improves the equivalent condition in recent literatures. Moreover, it also generalizes the well-known MacWilliams theorem of code equivalence.

Original language	English
Pages (from-to)	571-578
Number of pages	8
Journal	Information Sciences
Volume	221
DOIs	https://doi.org/10.1016/j.ins.2012.09.007
Publication status	Published - 1 Feb 2013

Keywords

Relative generalized Hamming weight
Relative projective subspace
Relative subcode
Semilinear code equivalence
Value assignment

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10.1016/j.ins.2012.09.007

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title = "Further results on the semilinear equivalence of linear codes",

abstract = "Based on relative subcodes, we address an equivalent condition for a one-to-one semilinear mapping between two linear codes to be in fact a semimonomial transformation, that is, the underlying two codes are semilinearly equivalent. The result in the present paper substantially improves the equivalent condition in recent literatures. Moreover, it also generalizes the well-known MacWilliams theorem of code equivalence.",

keywords = "Relative generalized Hamming weight, Relative projective subspace, Relative subcode, Semilinear code equivalence, Value assignment",

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AU - Zeng, Xiangyong

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N2 - Based on relative subcodes, we address an equivalent condition for a one-to-one semilinear mapping between two linear codes to be in fact a semimonomial transformation, that is, the underlying two codes are semilinearly equivalent. The result in the present paper substantially improves the equivalent condition in recent literatures. Moreover, it also generalizes the well-known MacWilliams theorem of code equivalence.

AB - Based on relative subcodes, we address an equivalent condition for a one-to-one semilinear mapping between two linear codes to be in fact a semimonomial transformation, that is, the underlying two codes are semilinearly equivalent. The result in the present paper substantially improves the equivalent condition in recent literatures. Moreover, it also generalizes the well-known MacWilliams theorem of code equivalence.

KW - Relative generalized Hamming weight

KW - Relative projective subspace

KW - Relative subcode

KW - Semilinear code equivalence

KW - Value assignment

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DO - 10.1016/j.ins.2012.09.007

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SN - 0020-0255

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SP - 571

EP - 578

JO - Information Sciences

JF - Information Sciences

ER -

Further results on the semilinear equivalence of linear codes

Abstract

Keywords

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