A construction of codes with linearity from two linear codes

Chengju Li; Sunghan Bae; Haode Yan

doi:10.1007/s12095-016-0193-6

A construction of codes with linearity from two linear codes

Chengju Li^*
, Sunghan Bae
, Haode Yan

^*Corresponding author for this work

Software Engineering Institute

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

7 Scopus citations

Abstract

Let F_p be a finite field, where p is a prime. This paper presents a new construction of a code C over F_p2 from two linear codes over F_p, which has F_p-linearity and its minimum distance is equal to its minimum nonzero weight. Based on our construction, we shall determine the weight enumerators of some codes defined by quadratic bent functions and simplex codes. It will be shown that these codes have a few nonzero weights.

Original language	English
Pages (from-to)	55-69
Number of pages	15
Journal	Cryptography and Communications
Volume	9
Issue number	1
DOIs	https://doi.org/10.1007/s12095-016-0193-6
State	Published - 1 Jan 2017

Keywords

Codes
Quadratic bent functions
Simplex codes
Weight enumerators

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10.1007/s12095-016-0193-6

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title = "A construction of codes with linearity from two linear codes",

abstract = "Let Fp be a finite field, where p is a prime. This paper presents a new construction of a code C over Fp2 from two linear codes over Fp, which has Fp-linearity and its minimum distance is equal to its minimum nonzero weight. Based on our construction, we shall determine the weight enumerators of some codes defined by quadratic bent functions and simplex codes. It will be shown that these codes have a few nonzero weights.",

keywords = "Codes, Quadratic bent functions, Simplex codes, Weight enumerators",

author = "Chengju Li and Sunghan Bae and Haode Yan",

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AU - Yan, Haode

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N2 - Let Fp be a finite field, where p is a prime. This paper presents a new construction of a code C over Fp2 from two linear codes over Fp, which has Fp-linearity and its minimum distance is equal to its minimum nonzero weight. Based on our construction, we shall determine the weight enumerators of some codes defined by quadratic bent functions and simplex codes. It will be shown that these codes have a few nonzero weights.

AB - Let Fp be a finite field, where p is a prime. This paper presents a new construction of a code C over Fp2 from two linear codes over Fp, which has Fp-linearity and its minimum distance is equal to its minimum nonzero weight. Based on our construction, we shall determine the weight enumerators of some codes defined by quadratic bent functions and simplex codes. It will be shown that these codes have a few nonzero weights.

KW - Codes

KW - Quadratic bent functions

KW - Simplex codes

KW - Weight enumerators

UR - https://www.scopus.com/pages/publications/85008312195

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DO - 10.1007/s12095-016-0193-6

M3 - 文章

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JO - Cryptography and Communications

JF - Cryptography and Communications

IS - 1

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A construction of codes with linearity from two linear codes

Abstract

Keywords

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