Linear codes with few weights from inhomogeneous quadratic functions

Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes with few weights are constructed from inhomogeneous quadrat...

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Bibliographic Details
Published in:Designs, codes, and cryptography Vol. 83; no. 3; pp. 691 - 714
Main Authors: Tang, Chunming, Xiang, Can, Feng, Keqin
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2017
Springer Nature B.V
Subjects:
Binary system
Circuits
Codes
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Linear codes
Quadratic equations
94B15
Weight distribution
94B35
94A24
Quadratic forms
Linear codes
94A55
Cyclotomic fields
ISSN:0925-1022, 1573-7586
Online Access:Get full text
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Summary:Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes with few weights are constructed from inhomogeneous quadratic functions over the finite field GF ( p ) , where p is an odd prime. They include some earlier linear codes as special cases. The weight distributions of these linear codes are also determined.
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ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-016-0267-7