Some connections between self-dual codes, combinatorial designs and secret sharing schemes

Stefka Bouyuklieva; Zlatko Varbanov

doi:10.3934/amc.2011.5.191

Article Contents

2011, Volume 5, Issue 2: 191-198. Doi: 10.3934/amc.2011.5.191

This issue Previous Article Large constant dimension codes and lexicodes Next Article Symmetric designs possessing tactical decompositions

Some connections between self-dual codes, combinatorial designs and secret sharing schemes

Stefka Bouyuklieva^1, and
Zlatko Varbanov^1,

1.
Department of Mathematics and Informatics, Veliko Tarnovo University

Received: February 28, 2010

Revised: June 30, 2010

Published: April 2011

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Abstract

In the present work we study a class of singly-even self-dual codes with the special property that the minimum weight of their shadow is 1. Some of these codes support 1 and 2-designs. Using them, we describe two types of schemes based on codes, the first is an one-part secret sharing scheme and the second is a two-part sharing scheme. Similar schemes can be constructed from self-dual codes that support 3-designs.

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Mathematics Subject Classification: Primary: 94B05, 94A62; Secondary: 05B05.

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References

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