环F_2+uF_2上的循环自正交码
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摘要
文章研究了环F_2+uF_2上长度为奇数的循环自正交码,其中u2=0;给出了F_2+uF_2上循环码的表示方法,得到了循环自正交码的生成多项式与计数公式;并确立了环F_2+uF_2上循环自对偶码的结构与数目。
Cyclic self-orthogonal codes over F_2+uF_2 of odd length are studied,where u2=0.A kind of representation of cyclic codes over F_2+uF_2 is given.The generator polynomial and enumeration formula of cyclic self-orthogonal codes over F_2+uF_2 are obtained.In particular,the structure and number of cyclic self-dual codes over F_2+uF_2 are determined.
Cyclic self-orthogonal codes over F_2+uF_2 of odd length are studied,where u2=0.A kind of representation of cyclic codes over F_2+uF_2 is given.The generator polynomial and enumeration formula of cyclic self-orthogonal codes over F_2+uF_2 are obtained.In particular,the structure and number of cyclic self-dual codes over F_2+uF_2 are determined.
引文
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[9]张付丽,开晓山,陈安顺.环F2m+uF2m上常循环码及其Gray像[J].合肥工业大学学报(自然科学版),2015,38(1):136-139.
[10]QIAN K Y,ZHU S X,KAI X S.On cyclic self-orthogonal codes over Z2m[J].Finite Fields and Their Applications,2015,33:53-65.
[2]BONNECAZE A,UDAYA P.Cyclic codes and self-dual codes over F2+uF2[J].IEEE Transactions on Information Theory,1999,45(4):1250-1255.
[3]UDAYA P,BONNECAZE A.Decoding of cyclic codes over F2+uF2[J].IEEE Transactions on Information Theory,1999,45(6):2148-2157.
[4]李平,朱士信.环F2+uF2上长为2e的循环码[J].电子信息学报,2007,29(5):1124-1126.
[5]DINH H Q.Constacyclic codes of length 2s over Galois extension rings of F2+uF2[J].IEEE Transactions on Information Theory,1999,55(4):1730-1740.
[6]CALDERBANK A R,RAINS E M,SHOR P W,et al.Quantum error correction via codes over GF(4)[J].IEEE Transactions on Information Theory,1998,44(4):1369-1387.
[7]ALY S A,KLAPPENECKER A,SARVEPALLI P K.On quantum and classical BCH codes[J].IEEE Transactions on Information Theory,2007,53(3):1183-1188.
[8]张付丽,开晓山,朱士信,等.一种有限域上自正交码的构造方法[J].电子与信息学报,2014,36(10):2326-2330.
[9]张付丽,开晓山,陈安顺.环F2m+uF2m上常循环码及其Gray像[J].合肥工业大学学报(自然科学版),2015,38(1):136-139.
[10]QIAN K Y,ZHU S X,KAI X S.On cyclic self-orthogonal codes over Z2m[J].Finite Fields and Their Applications,2015,33:53-65.