摘要
利用 R（pm ，k）＝ Fpm [u]／＜ uk ＞上任意长度的（1＋λu）常循环码的挠码得到了 R（ pm ，k）上任意长度的（1＋λu）常循环码的齐次距离的界，并确定了 R（pm ，k）上某些（1＋λu）常循环码的齐次距离的准确值，其中λ是R（ pm ，k）上的单位。此外，定义了从 RN（pm ，k）（Homogeneous 距离）到 F pm（k －1） N pm （Hamming 距离）的一个新的保距Gray 映射，得到 R（pm ，k）上任意长度的线性（1＋λu）常循环码的 Gray 像是 Fpm 上的线性码，构造了 F2、 F3和F4上的一些最优线性码。
Abstract
Based on the torsion codes of a (1 + λu)constacyclic code with arbitrary length over R(pm ,k) = Fpm [u]/< uk > ,a bound for the homogeneous distance of a (1 + λu) constacyclic code with an arbitrary length over R( pm ,k) is obtained and the exact homogeneous distances of some (1 + λu) constacyclic codes over R( pm ,k) are determined ,where λ is a unit of R(pm ,k) .Furthermore , a new distance‐preserving Gray map from R N ( pm ,k) (Homogeneous distance) to F pm(k - 1) N pm (Hamming distance) is defined .It is proved that the Gray image of a linear (1 + λu) constacyclic code of arbitrary length over R(pm ,k) is a linear code over Fpm ,and some optimal linear codes over F2 ,F3 , and F4 are constructed under this Gray map .
基金项目
Supported by National Natural Science Foundation of China(61370089)
Anhui Province Natural Science Research(KJ2015A308)
Natural Science Project of AnHui Xinhua University(2014Zr009)
NETL
NSTL
维普
万方数据