Session S29 - Theory and Applications of Coding Theory

Tuesday, July 13, 14:00 ~ 14:25 UTC-3

Additive twisted codes and new infinite families of binary quantum codes

Reza Dastbasteh

Simon Fraser University , Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We study a subclass of additive cyclic codes called the additive twisted codes, which were introduced by Bierbrauer and Edel (1997). The twisted codes inherit many properties of linear cyclic codes such as the BCH minimum distance bound. We show that many other well-known minimum distance bounds for the linear cyclic codes including Hartman-Tzeng, Roos, and van Lint-Wilson minimum distance bounds all remain valid for the twisted codes.

A novel minimum distance condition for the twisted codes with a symmetric defining set is also provided. This result leads to new infinite classes of twisted codes with the minimum distance five. Following that, several new infinite families of good binary quantum codes with the minimum distances four and five are constructed.

J. Bierbrauer and Y. Edel: Quantum twisted codes, Journal of Combinatorial Designs 8 (2000), 174-188.

Y. Edel and J. Bierbrauer: Twisted BCH-codes, Journal of Combinatorial Designs 5 (1997), 377-389.

Joint work with Petr Lisonek (Simon Fraser University).

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