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Designs, Codes and Cryptography

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15.03.2017

Infinite families of 3-designs from a type of five-weight code

verfasst von: Cunsheng Ding

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2018

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Abstract

It has been known for a long time that t-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a t-design. While a lot of progress in the direction of constructing codes from t-designs has been made, only a small amount of work on the construction of t-designs from codes has been done. The objective of this paper is to construct infinite families of 2-designs and 3-designs from a type of binary linear codes with five weights. The total number of 2-designs and 3-designs obtained in this paper are exponential in any odd m and the block size of the designs varies in a huge range.

Vorheriger Artikel New families of balanced symmetric functions and a generalization of Cusick, Li and Stǎnicǎ’s conjecture

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Titel: Infinite families of 3-designs from a type of five-weight code
verfasst von: Cunsheng Ding
Publikationsdatum: 15.03.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0352-6

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