环F_2+uF_2+u~2F_2上循环码的Gray距离
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摘要
定义了环R=F2+uF2+u2 F2(u3=0)到F32的一个新的Gray映射.首先介绍环R上奇长度的循环码的挠码,给出了各阶挠码的生成多项式.利用一阶挠码与二阶挠码确立了R上奇长度的循环码的Gray距离.
A new Gray map is defined fromR = F2 +uF2 +u2 F2 to F32,where u3=0.The torsion codes of cyclic codes over Rof odd length are introduced,and the generator polynomials of the torsion codes are given.In terms of the first and second torsion codes,the Gray distance of cyclic codes over Rof odd length is determined.
A new Gray map is defined fromR = F2 +uF2 +u2 F2 to F32,where u3=0.The torsion codes of cyclic codes over Rof odd length are introduced,and the generator polynomials of the torsion codes are given.In terms of the first and second torsion codes,the Gray distance of cyclic codes over Rof odd length is determined.
引文
[1]Hammons Jr A R,Kumar P V,Calderbank A R,et al.The Z4-linearity of Kerdock,Preparata,Goethals,and related codes[J].IEEE Transactions on Information Theory,1994,40(2):301-319.
[2]Wolfman J.Negacyclic and cyclic codes over Z4[J].IEEE Transactions on Information Theory,1999,45(7):2527-2532.
[3]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.
[4]朱士信,李平,吴波.环Fq+uFq+…+uk-1Fq上一类重根常循环码[J].电子与信息学报,2008,30(6):1394-1396.
[5]Dinh H Q,Nguyen H D T.On some classes of constacyclic codes over polynomial residue rings[J].Advances in Mathematics of Communications,2012,6(2):175-191.
[6]Bonnecaze A,Udaya P.Cyclic codes and self-dual codes over F2+uF2[J].IEEE Transactions on Information Theory,1999,45(4):1250-1255.
[7]Dinh H Q,López-Permouth S R,Cyclic and negacyclic codes over finite chain rings[J].IEEE Transactions on Information Theory,2004,50(8):1728-1744.
[2]Wolfman J.Negacyclic and cyclic codes over Z4[J].IEEE Transactions on Information Theory,1999,45(7):2527-2532.
[3]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.
[4]朱士信,李平,吴波.环Fq+uFq+…+uk-1Fq上一类重根常循环码[J].电子与信息学报,2008,30(6):1394-1396.
[5]Dinh H Q,Nguyen H D T.On some classes of constacyclic codes over polynomial residue rings[J].Advances in Mathematics of Communications,2012,6(2):175-191.
[6]Bonnecaze A,Udaya P.Cyclic codes and self-dual codes over F2+uF2[J].IEEE Transactions on Information Theory,1999,45(4):1250-1255.
[7]Dinh H Q,López-Permouth S R,Cyclic and negacyclic codes over finite chain rings[J].IEEE Transactions on Information Theory,2004,50(8):1728-1744.