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

Jianying Fang | Zendy

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

Author(s) -

Jianying Fang

Publication year - 2017

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2017017

Subject(s) - binary golay code , mathematics , disjoint sets , circulant matrix , lambda , code (set theory) , combinatorics , generator (circuit theory) , generator matrix , discrete mathematics , arithmetic , algorithm , decoding methods , physics , quantum mechanics , computer science , power (physics) , set (abstract data type) , programming language

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 $G_{24}$.

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