利用齐次距离构造最优码（英文）
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摘要
利用R(pm,k)=Fpm[u]/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Fpm(k-1)Npm(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.
Based on the torsion codes of a(1+λu)constacyclic code with arbitrary length over R(mp,k)=Fmp[u]/,a bound for the homogeneous distance of a(1+λu)constacyclic code with an arbitrary length over R(mp,k)is obtained and the exact homogeneous distances of some(1+λu)constacyclic codes over R(mp,k)are determined,whereλis a unit of R(mp,k).Furthermore,m(k-1)a new distance-preserving Gray map from RN p(mp,mN k)(Homogeneous distance)to Fp(Hamming distance)is defined.It is proved that the Gray image of a linear(1+λu)constacyclic code of arbitrary length over R(mp,k)is a linear code over Fmp,and some optimal linear codes over F2,F3,and F4 are constructed under this Gray map.
Based on the torsion codes of a(1+λu)constacyclic code with arbitrary length over R(mp,k)=Fmp[u]/
引文
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[2]施敏加,杨善林,朱士信.环F2[u]/
[3]刘晓娟,朱士信.环Fpm+uFpm+…+uk-1Fpm上的长为ps的(1+λu)常循环码的距离分布[J].中国科学技术大学学报,2012,42(11):931-935.Liu X J,Zhu S X.The distributions of distances of(1+λu)constacyclic codes of length ps over Fpm+uFpm+…+uk-1Fpm[J].Journal of University of Science and Technology of China,2012,42(11):931-935.
[4]朱士信,黄素娟.环Fpm+uFpm+…+uk-1 Fpm上(1+u)常循环码的齐次距离分布[J].电子与信息学报,2013,35(11):2579-2583.Zhu S X,Huang S J.The distribution of homogeneous distance of(1+u)constacyclic codes over Fpm+uFpm+…+uk-1 Fpm[J].Journal of Electronics&Information Technology,2013,35(11):2579-2583.
[5]Qian J F,Zhang L N,Zhu S X.(1+u)constacyclic and cyclic codes over F2+uF2[J].Applied Mathematics Letters,2006,19(8):820-823.
[6]Ding J,Li H J.The Gray images of-constacyclic codes over F2m[u]/
[7]Ding J,Li H J.The Gray image of a class of constacyclic codes over polynomial residue rings[J].Journal of the Franklin Institute,2014,351(12):5467-5479.
[8]Kai X S,Zhu S X,Li P.(1+λu)constacyclic codes over Fp[u]/
[9]Amarra M C V,Nemenzo F R.On(1+u)cyclic codes over Fpk+uFpk[J].Applied Mathematics Letters,2008,21(11):1129-1133.
[10]Sobhani R,Esmaeili M.Some constacyclic and cyclic codes over Fq[u]/
[11]Udomkavanich P,Jitman S.On the gray image of(1+um)cyclic codes over Fpk+uFpk+…+umFpk[J].International Journal of Contemporary Mathematical Sciences,2009,4(25):1265-1272.
[12]Greferath M,Schmidt S E.Gray isometries for finite chain rings and a nonlinear ternary(36,312,15)code[J].IEEE Transactions on Information Theory,1999,45(7):2522-2524.
[13]李岩,朱士信.环Fpm+uFpm+…+uk-1Fpm上的一类常循环码[J].合肥工业大学学报,2013,35(3):408-411.Li Y,Zhu S X.A class of constacyclic codes over the ring Fpm+uFpm+…+uk-1Fpm[J].Journal of Hefei University of Technology,2013,35(3):408-411.
[14]Han M,Ye Y P,Zhu S X,et al.Cyclic codes over R=Fpm+uFpm+…+uk-1 Fpm with psn length[J].Information Science,2011,181(4):926-934.
[15]Sǎlǎgean A.Repeated-root cyclic and negacyclic codes over a finite chain ring[J].Discrete Applied Mathematics,2005,154(2):413-419.