共查询到20条相似文献,搜索用时 62 毫秒
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循环码作为一类重要的线性码,因其有效的编码和译码算法而被广泛应用于通信和存储系统.令F_r为有限域F_q的一个扩域,其中r=q~m,α为有限域F_r的本原元.设n=n1n2满足gcd(n1,n2)=1为r-1的因子.定义F_q上的一类循环码C={c(a1,a2)=(T_r/q(a1y_1~2+a2(g1g2)~i))_(i=0)~(n-1):a1,a2∈F_r},其中g1=α(r-1)/(n1),g2=α(r-1)/(n2),且g1与g1g2不共轭.本文将利用Gauss周期刻画循环码C的权重分布.特别地,这类循环码包含一类二重循环码和一类三重循环码. 相似文献
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从另一种角度研究了有限链环上循环码.给出了这种环上循环码的构造由这种构造得到了有限链环上的循环码的生成多项式.借助有限链环上循环码与负循环码的同构,也得到了这种环上循环码的生成元. 相似文献
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研究了有限链环R上常循环码的等价性,根据等价性给出了R上一些常循环码及其对偶码的结构.确定了该环上长度为ps的所有常循环码及其对偶码的结构. 相似文献
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文章研究了有限环R=F_p+vF_p上一类任意长度的θ-常循环码的周期分布,其中v~2=v和θ=λ+v u.利用环R上θ-常循环码的结构的分解,将该环上这类常循环码的周期转化成两个对应的常循环码的周期的乘积. 相似文献
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一类循环码的极小距离 总被引:1,自引:0,他引:1
循环码的极小距离大于或等于BCH界。本文考虑的是极小距离等于BCH界的特殊情形。利用一类自反循环码的事实。证明了使循环码的极小距离等于其BCH界的两个充分条件;并指出极小距离等于任意给定值,维数任意大的循环码可以构造。 相似文献
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本文研究了有限非链环Fp+vFp上的负循环码和v-常循环码的结构.利用中国剩余定理给出了该环上负循环码和Fp上负循环码的关系并证明了该环上n长的负循环码可以由Fp+vFp上次数小于或等于n-1的多项式生成,得到了该环上n长的u-常循环码也是(Fp+vFp)[x]/的主理想. 相似文献
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研究给出了一类基于循环码的常重复合码的构造,并利用指数和计算其参数.与相关的常重复合码相比,该码具有更多的码字,且渐近性较好. 相似文献
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记环R=F_(p~k)+uF_(p~k)+u~2F_(p~k),定义了一个从R~n到F_(p~k)~(2np~k)的Gray映射.利用Gray映射的性质,研究了环R上(1-u~2)-循环码和循环码.证明了环R上码是(1-u~2)-循环码当且仅当它的Gray象是F_(p~k)上的准循环码.当(n,p)=1时,证明了环R上的长为n的线性循环码的Gray象置换等价于域F_(p~k)上的线性准循环码. 相似文献
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Weight distribution of some reducible cyclic codes 总被引:1,自引:1,他引:0
Let q=pm where p is an odd prime, m3, k1 and gcd(k,m)=1. Let Tr be the trace mapping from to and . In this paper we determine the value distribution of following two kinds of exponential sums and where is the canonical additive character of . As an application, we determine the weight distribution of the cyclic codes and over with parity-check polynomial h2(x)h3(x) and h1(x)h2(x)h3(x), respectively, where h1(x), h2(x) and h3(x) are the minimal polynomials of π−1, π−2 and π−(pk+1) over , respectively, for a primitive element π of . 相似文献
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Anuradha Sharma Gurmeet K. Bakshi Madhu Raka 《Finite Fields and Their Applications》2007,13(4):1086-1095
Let m be a positive integer and q be an odd prime power. In this paper, the weight distributions of all the irreducible cyclic codes of length 2m over Fq are determined explicitly. 相似文献
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Combinatorial ‐designs have wide applications in coding theory, cryptography, communications, and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a ‐design. In this paper, we first determine the weight distributions of a class of linear codes derived from the dual of some extended cyclic codes. We then obtain infinite families of 2‐designs and explicitly compute their parameters from the supports of all the codewords with a fixed weight in the codes. By a simple counting argument, we obtain exponentially many 2‐designs. 相似文献
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Let be the Galois ring of characteristic and cardinality . Firstly, we give all primitive idempotent generators of irreducible cyclic codes of length over , and a -adic integer ring with . Secondly, we obtain all primitive idempotents of all irreducible cyclic codes of length over , where and are three primes with , , and . Finally, as applications, weight distributions of all irreducible cyclic codes for and generator polynomials of self-dual cyclic codes of length and over are given. 相似文献
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Cyclic codes have attracted a lot of research interest for decades as they have efficient encoding and decoding algorithms. In this paper, for an odd prime p, we investigate two classes of p-ary cyclic codes for special cases and determine their weight distributions explicitly. The results show that both codes have at most five nonzero weights. 相似文献