A FAMILY OF CONSTACYCLIC CODES OVER F2 + uF2 + vF2 + uvF2

Xiaoshan KAI , Shixin ZHU , Liqi WANG

Journal of Systems Science & Complexity ›› 2012, Vol. 25 ›› Issue (5) : 1032-1040.

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Journal of Systems Science & Complexity ›› 2012, Vol. 25 ›› Issue (5) : 1032-1040. DOI: 10.1007/s11424-012-1001-9
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A FAMILY OF CONSTACYCLIC CODES OVER F2 + uF2 + vF2 + uvF2

  • Xiaoshan KAI 1, Shixin ZHU 1, Liqi WANG2
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Abstract

This paper studies (1 + u)-constacyclic codes over the ring F2 + uF2 + vF2 + uvF2. It is proved that the image of a (1+u)-constacyclic code of length n over F2+uF2+vF2+uvF2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined. Some optimal binary codes are obtained directly from (1 + u)-constacyclic codes over F2 + uF2 + vF2 + uvF2.

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Xiaoshan KAI , Shixin ZHU , Liqi WANG. A FAMILY OF CONSTACYCLIC CODES OVER F2 + uF2 + vF2 + uvF2. Journal of Systems Science and Complexity, 2012, 25(5): 1032-1040 https://doi.org/10.1007/s11424-012-1001-9

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This research was supported by the National Natural Science Foundation of China under Grant No. 60973125, the Natural Science Foundation of Anhui Province under Grant No. 1208085MA14, and the Fundamental Research Funds for the Central Universities under Grants Nos. 2012HGXJ0040 and 2011HGBZ1298.

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