Complete weight enumerators of some linear codes from quadratic forms

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q -ary linear codes with few weights employing general quadratic forms over the finite field F q is proposed, where q is an odd...

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Bibliographic Details
Published inCryptography and communications Vol. 9; no. 1; pp. 151 - 163
Main Authors Zhang, Dan, Fan, Cuiling, Peng, Daiyuan, Tang, Xiaohu
Format Journal Article
LanguageEnglish
Published New York Springer US 01.01.2017
Springer Nature B.V
Subjects
Binary system
Circuits
Codes
Coding and Information Theory
Communications Engineering
Computer Science
Data Structures and Information Theory
Information and Communication
Linear codes
Mathematics of Computing
Networks
Quadratic forms
94B15
Weight distribution
94B35
94A24
Codes with few weights
Linear codes
Quadratic form
Complete weight enumerator
94A55
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Summary:Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q -ary linear codes with few weights employing general quadratic forms over the finite field F q is proposed, where q is an odd prime power. This generalizes some earlier constructions of p -ary linear codes from quadratic bent functions over the prime field F p , where p is an odd prime. The complete weight enumerators of the resultant q -ary linear codes are also determined.
ISSN:1936-2447
1936-2455
DOI:10.1007/s12095-016-0190-9