Complete weight enumerators of a family of three-weight linear codes

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime p , we present the explicit complete weight enumerator of a family of p -ary linear codes constructed with defining set. The weight enumerator is an immediate result of the complet...

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Veröffentlicht in:	Designs, codes, and cryptography codes, and cryptography, 2017-03, Vol.82 (3), p.663-674
Hauptverfasser:	Yang, Shudi, Yao, Zheng-An
Format:	Artikel
Sprache:	eng
Schlagworte:	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
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Zusammenfassung:	Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime p , we present the explicit complete weight enumerator of a family of p -ary linear codes constructed with defining set. The weight enumerator is an immediate result of the complete weight enumerator, which shows that the codes proposed in this paper are three-weight linear codes. Additionally, all nonzero codewords are minimal and thus they are suitable for secret sharing.
ISSN:	0925-1022 1573-7586
DOI:	10.1007/s10623-016-0191-x