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 in:Cryptography and communications 2017-01, Vol.9 (1), p.151-163
Main Authors: Zhang, Dan, Fan, Cuiling, Peng, Daiyuan, Tang, Xiaohu
Format: Article
Language:English
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
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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