This paper introduces a Gray map from （Fp ＋ vFp）n to F2pn, and describes the relationship between codes over Fp ＋ vFp and their Gray images. The authors prove that every cyclic code of arbitrary length n over Fp ...This paper introduces a Gray map from （Fp ＋ vFp）n to F2pn, and describes the relationship between codes over Fp ＋ vFp and their Gray images. The authors prove that every cyclic code of arbitrary length n over Fp ＋ vFp is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.展开更多
基金supported by NNSF of China under Grant Nos.11126174,60973125,71071045 and 71001032Talents youth Fund of Anhui Province Universities under Grant No.2012SQRL020ZD+1 种基金Youth Science Research Fund of Anhui University under Grant No.2009QN026Bthe 211 Project of Anhui University Grant No. KJTD002B
文摘This paper introduces a Gray map from （Fp ＋ vFp）n to F2pn, and describes the relationship between codes over Fp ＋ vFp and their Gray images. The authors prove that every cyclic code of arbitrary length n over Fp ＋ vFp is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.
