共查询到20条相似文献,搜索用时 15 毫秒
1.
Jürgen Bierbrauer 《Designs, Codes and Cryptography》2002,25(2):189-206
We present a new approach to the theory of cyclic and constacyclic codes and generalize the theory to cover the family of additive (not necessarily linear) cyclic codes. The approach is based on the action of the Galois group (cyclotomic cosets). The conventional representation of cyclic codes as ideals in a factor ring of the polynomial ring is not needed. 相似文献
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Axel Kohnert 《Discrete Applied Mathematics》2007,155(11):1451-1457
We construct new linear two-weight codes over the finite field with q elements. To do so we solve the equivalent problem of finding point sets in the projective geometry with certain intersection properties. These point sets are in bijection to solutions of a Diophantine linear system of equations. To reduce the size of the system of equations we restrict the search for solutions to solutions with special symmetries.Two-weight codes can be used to define strongly regular graphs. We give tables of the two-weight codes and the corresponding strongly regular graphs. In some cases we find new distance-optimal two-weight codes and also new strongly regular graphs. 相似文献
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It is known that a projective linear two-weight code C over a finite field corresponds both to a set of points in a projective space over that meets every hyperplane in either a or b points for some integers a < b, and to a strongly regular graph whose vertices may be identified with the codewords of C. Here we extend this classical result to the case of a ring-linear code with exactly two nonzero homogeneous weights and
sets of points in an associated projective ring geometry. We will introduce regular projective two-weight codes over finite
Frobenius rings, we will show that such a code gives rise to a strongly regular graph, and we will give some constructions
of two-weight codes using ring geometries. All these examples yield infinite families of strongly regular graphs with non-trivial
parameters.
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5.
Designs, Codes and Cryptography - Projective two-weight linear codes are closely related to finite projective spaces and strongly regular graphs. In this paper, a family of q-ary two-weight linear... 相似文献
6.
We introduce and solve several problems on
-cyclic codes.We study the link between
-linear cyclic codes and
-cyclic codes (not necessarily linear) obtained by using two binary linear cyclic codes. We use these results to present a family of
-self-dual linear cyclic codes. 相似文献
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《Finite Fields and Their Applications》2002,8(1):1-17
The aim of this paper is the classification of two-weight irreducible cyclic codes. Using Fourier transforms and Gauss sums, we obtain necessary and sufficient numerical conditions for an irreducible cyclic code to have at most two weights. This gives a unified explanation for all two-weight irreducible cyclic codes and allows a conjecturally complete classification. Aside from the two known infinite families of two-weight irreducible cyclic codes, a computer search reveals 11 sporadic examples. We conjecture that these are already all two-weight irreducible cyclic codes and give a partial proof of our conjecture conditionally on GRH. 相似文献
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One of the most important problems of coding theory is to constructcodes with best possible minimum distances. In this paper, we generalize the method introduced by [8] and obtain new codes which improve the best known minimum distance bounds of some linear codes. We have found a new linear ternary code and 8 new linear codes over
with improved minimumdistances. First we introduce a generalized version of Gray map,then we give definition of quasi cyclic codes and introduce nearlyquasi cyclic codes. Next, we give the parameters of new codeswith their generator matrices. Finally, we have included twotables which give Hamming weight enumerators of these new codes. 相似文献
10.
José Gómez-Torrecillas F. J. Lobillo Gabriel Navarro 《Linear and Multilinear Algebra》2018,66(3):469-487
We design a non-commutative version of the Peterson–Gorenstein–Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In particular, our decoding algorithm applies for block codes beyond the classical cyclic case. 相似文献
11.
We determine the structure of cyclic codes over
for arbitrary even length giving the generator polynomial for these codes. We determine the number of cyclic codes for a
given length. We describe the duals of the cyclic codes, describe the form of cyclic codes that are self-dual and give the
number of these codes. We end by examining specific cases of cyclic codes, giving all cyclic self-dual codes of length less
than or equal to 14.
San Ling - The research of the second named author is partially supported by research Grants MOE-ARF R-146-000-029-112 and
DSTA R-394-000-011-422. 相似文献
12.
We introduce new classes of 2-weight cyclic codes which are direct sums of 1-weight irreducible cyclic codes
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13.
We show by a combination of theoretical argument and computer search that if a projective (75, 4, 12, 5) set in PG(3, 7) exists then its automorphism group must be trivial. This corresponds to the smallest open case of a coding problem posed by H. Ward in 1998, concerning the possible existence of an infinite family of projective two-weight codes meeting the Griesmer bound. 相似文献
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本文研究了环F2 uF2上的奇长度的循环码和(1 u)-循环码.运用代数方法,得到了F2 uF2上的循环码和(1 u)-循环码成为自由码的几个充要条件.推广了Bonnecaze(1999)和Aydin(2002)的关于自由码的结果. 相似文献
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In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m + uFp^m, where p is an odd prime. On the basis of the works of Dinh (in J.Algebra 324,940-950,2010), we use the Chinese Remainder Theorem to establish the algebraic structure of cyclic and negacyclic codes of length 2p^s over the ring Fp^m + uFp^m in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes. 相似文献
17.
In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained. 相似文献
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In this paper, we construct some codes that arise from generalized hexagons with small parameters. As our main result we discover
two new projective two-weight codes constructed from two-character sets in PG(5,4) and PG(11,2). These in turn are constructed using a new distance-2-ovoid of the classical generalized hexagon H(4). Also the corresponding strongly regular graph is new. The two-character set is the union of two orbits in PG(5,4) under the action of L2(13).
Communicated by: R. Calderbank
The first Author is Research Assistant of the Fund for Scientific Research - Flanders (Belgium) (F.W.O) 相似文献
20.
Jacques Wolfmann 《Journal of Combinatorial Theory, Series A》1977,23(2):208-222
Using certain sets of points of a finite projective geometry some results are obtained from properties of two-weight projective codes. A problem concerning complete caps is solved. A deep connection between binary uniformily packed codes and difference sets over elementary Abelian 2-groups is established and a characterization of these difference sets is given. 相似文献