Paper 2015/1103

Linear codes with few weights from weakly regular bent functions based on a generic construction

Sihem Mesnager

Abstract

We contribute to the knowledge of linear codes with few weights from special polynomials and functions. Substantial eorts (especially due to C. Ding) have been directed towards their study in the past few years. Such codes have several applications in secret sharing, authentication codes, association schemes and strongly regular graphs. Based on a generic construction of linear codes from mappings and by employing weakly regular bent functions, we provide a new class of linear p-ary codes with three weights given with its weight distribution. The class of codes presented in this paper is dierent from those known in literature. Also, it contains some optimal codes meeting certain bound on linear codes.

Metadata
Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
Linear codesweight distributionp-ary functionsbent functionsweakly regular bent functionsvectorial functionscyclotomic fields
Contact author(s)
smesnager @ univ-paris8 fr
History
2015-12-11: last of 6 revisions
2015-11-14: received
See all versions
Short URL
https://ia.cr/2015/1103
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/1103,
      author = {Sihem Mesnager},
      title = {Linear codes with few weights from weakly regular bent functions based on a generic construction},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/1103},
      year = {2015},
      url = {https://eprint.iacr.org/2015/1103}
}
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