环k_q+uF_q+…+u~(k-1)F_q上任意长度的(uλ-1)-常循环码
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摘要
该文利用环同态理论,给出了环kq+uFq+…+u(k-1)Fq上任意长度N的所有(uλ-1)-常循环码的生成元,l是R的可逆元。证明了R[x]/1是主理想环。给出了环R上任意长度N的(uλ-1)-常循环码的计数。确定了环R上任意长度N的(uλ-1)-常循环码的最高阶挠码的生成多项式,由此给出了环R上长度ps的所有(uλ-1)-常循环码的汉明距离。
Let R denote the ring kq+uFq+…+u(k-1)Fq,and λ be an invertible element of R.By means of the theory of ring homomorphism,the generators of all these(uλ-1)-constacyclic codes of an arbitrary length N over the ring R are obtained.It is proved that R[x]/1 is principal.The number of these(uλ-1)-constacyclic codes is determined.The generator polynomials of the highest-order torsion codes of all these(uλ-1)-constacyclic codes are given.As a result,the Hamming distances of all these(uλ-1) constacyclic codes are obtained.
Let R denote the ring kq+uFq+…+u(k-1)Fq,and λ be an invertible element of R.By means of the theory of ring homomorphism,the generators of all these(uλ-1)-constacyclic codes of an arbitrary length N over the ring R are obtained.It is proved that R[x]/1
引文
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[2]Kai Xiao-shan,Zhu Shi-xin,and Li Ping.(1+ul)-constacyclic codes over[]/m p F u[J].Journal of the Franklin Institute,2010,347(3):751-762.
[3]Han Mu,Ye You-pei,Zhu Shi-xin,et al..Cyclic codes over F1+UF1+…+ut-1Ft with length spn[J].Information Sciences,2011,181(4):926-934.
[4]朱士信,李平,吴波.环kq+uFq+…+u(k-1)Fq上一类重根常循环码[J].电子与信息学报,2008,30(6):1394-1396.Zhu Shi-xin,Li Ping,and Wu Bo.A class of repeated-root constacyclic codes over the ring kq+uFq+…+u(k-1)Fq[J].Journal of Electronics&Information Technology,2008,30(6):1394-1396.
[5]Dinh H Q.Constacyclic codes of length2 s over Galois extension rings of 22 F+uF[J].IEEE Transactions on Information Theory,2009,55(4):1730-1740.
[6]施敏加,杨善林,朱士信.环F2+uF2+…+Ut-1F2上长为2 s的(1+u)-常循环码的距离分布[J].电子与信息学报,2010,32(1):112-116.Shi Min-jia,Yang Shan-lin,and Zhu Shi-xin.The distributions of distances of(1+u)-constacyclic codes of length2 s over 1 222 k F uF u F-+++[J].Journal of Electronics&Information Technology,2010,32(1):112-116.
[7]Jitman S.Skew constacyclic codes over finite chain rings[J].Advances in Mathematics of Communications,2012,6(1):39-63.
[8]Dougherty S T,Karadeniz S,and Yildiz B.Cyclic codes over k R[J].Designs,Codes and Crypytography,2012,63(1):113-126.
[9]Yildiz B and Karadeniz S.Cyclic codes over F2+UF2+VF2+UVF2[J].Designs,Codes and Crypytography,2011,58(3):221-234.
[10]Dinh H Q.On some classes of constacyclic codes over polynomial residue rings[J].Advances in Mathematics of Communications,2012,6(2):175-191.
[11]Kai Xiao-shan and Zhu Shi-xin.Negacyclic self-dual codes over finite chain rings[J].Designs,Codes and Crypytography,2012,62(2):161-174.
[12]Norton G H and Sǎlǎgean A.On the structure of linear and cyclic codes over a finite chain ring[J].Applicable Algebra in Engineering,Communication and Computing,2000,10(2):489-506.
[13]Dougherty S T,Kim Jon-lark,and Liu Hong-wei.Constructions of self-dual codes over finite commutative chain rings[J].International Journal of Information and Coding Theory,2010,1(2):171-190.
[14]Dinh H Q.On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions[J].Finite Fields and Their Applications,2008,14(1):22-40.