Cryptology ePrint Archive: Report 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 e orts (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 di erent from those known in literature. Also, it contains some optimal codes meeting certain bound on linear codes.

Category / Keywords: Linear codes, weight distribution, p-ary functions, bent functions, weakly regular bent functions, vectorial functions, cyclotomic fields

Date: received 12 Nov 2015, last revised 10 Dec 2015

Contact author: smesnager at univ-paris8 fr

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Version: 20151211:044517 (All versions of this report)

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