5-SEEDs from the lifted Golay code of length 24 over Z4

Jianying Fang

doi:10.3934/amc.2017017

Article Contents

2017, Volume 11, Issue 1: 259-266. Doi: 10.3934/amc.2017017

This issue Previous Article Some results on the structure of constacyclic codes and new linear codes over GF(7) from quasi-twisted codes Next Article

5-SEEDs from the lifted Golay code of length 24 over Z₄

Jianying Fang

Institute of Computer Information Engineering, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

Received: November 2015

Published online: February 2017

The author is supported by NSFC grant 11401271, 61462026, 61262015, 61462040.

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Abstract

Spontaneous emission error designs (SEEDs) are combinatorial objects that can be used to construct quantum jump codes. The lifted Golay code $G_{24}$ of length $24$ over $\mathbb{Z}_4$ is cyclic self-dual code. It is known that $G_{24}$ yields $5$-designs. In this paper, by using the generator matrices of bordered double circulant codes, we obtain $22$ mutually disjoint $5$-$(24, k, \lambda)$ designs with $(k, \lambda)=(8, 1), $ $(10, 36), $ $(12,1584)$ and $5$-$(24, k;22)$-SEEDs for $k=8, $ $10, $ $12, $ $13$ from $G_{24}$.

Keywords:

Spontaneous emission error design (SEED),
lifted Golay code,
double circulant code,
mutually disjoint t-design,
cyclic code.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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