This paper studies （1 ＋ u）-constacyelic codes over the ring F2 ＋ uF2 ＋ vF,2 ＋ 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 di...This paper studies （1 ＋ u）-constacyelic codes over the ring F2 ＋ uF2 ＋ vF,2 ＋ 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.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.60973125the Natural Science Foundation of Anhui Province under Grant No.1208085MA14the Fundamental Research Funds for the Central Universities under Grants Nos.2012HGXJ0040 and 2011HGBZ1298
文摘This paper studies （1 ＋ u）-constacyelic codes over the ring F2 ＋ uF2 ＋ vF,2 ＋ 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.
