共查询到20条相似文献,搜索用时 0 毫秒
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Akihiro Munemasa 《Designs, Codes and Cryptography》1995,5(3):253-259
LetG be a finite abelian group,t a positive integer. Thet-shift sphere with centerx G is the setS
t
(x)={±ix|i=1,...,t}. At-shift code is a subsetX ofG such that the setsS
t
(x) (x X) have size 2t and are disjoint. Clearly, the sphere packing bound: 2t|X|+1|G| holds for anyt-shift codeX. Aperfect t-shift code is at-shift codeX with 2t|X|+1=|G|. A necessary and sufficient condition for the existence of a perfectt-shift code in a finite abelian group is known fort-1, 2. In this paper, we determine finite abelian groups in which there exists a perfectt-shift code fort=3, 4.This research was completed during the author's visit at the Institute for System Analysis, Moscow, as a Heizaemon Honda fellow of the Japan Association for Mathematical Sciences. 相似文献
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In this note, we prove that if C is a duadic binary abelian code with splitting μ=μ−1 and the minimum odd weight of C satisfies d2−d+1≠n, then d(d−1)n+11. We show by an example that this bound is sharp. A series of open problems on this subject are proposed. 相似文献
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Archiv der Mathematik - 相似文献
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Robert L Miller 《Journal of Combinatorial Theory, Series A》1979,26(2):166-178
In this paper we show that two minimal codes 1 and 2 in the group algebra 2[G] have the same (Hamming) weight distribution if and only if there exists an automorphism θ of G whose linear extension to 2[G] maps 1 onto 2. If θ(M1) = M2, then 1 and 2 are called equivalent. We also show that there are exactly τ(l) inequivalent minimal codes in 2[G], where ? is the exponent of G, and τ(?) is the number of divisors of ?. 相似文献
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V. G. Sargsyan 《Journal of Applied and Industrial Mathematics》2013,7(4):574-587
A subset A of elements in an abelian group G is called k-zero-free if the equation x 1 + x 2 + ... + x k = 0 has no solution in A. A k-zero-free set A in G is called maximal if A ∪ {x} is k-zero-free for no x ∈ G\A. Some bounds for the maximum size of a k-zero free set are obtained. In particular, we determine the maximum speed of a k-zero-free arithmetic progression in the cyclic group Z n and find the upper and lower bounds for the maximum size of a k-zero-free set in an abelian group G. We describe the structure of a maximal k-zero-free set A in the cyclic group Z n provided that gcd(n, k) = 1 and k|A| ≥ n + 1. 相似文献
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In 1998 Høholdt, van Lint and Pellikaan introduced the concept of a “weight function” defined on a \({\mathbb{F}_q}\)-algebra and used it to construct linear codes, obtaining among them the algebraic geometry (AG) codes supported on one point. Later, in 1999, it was proved by Matsumoto that all codes produced using a weight function are actually AG codes supported on one point. Recently, “near weight functions” (a generalization of weight functions), also defined on a \({\mathbb{F}_q}\)-algebra, were introduced to study codes supported on two points. In this paper we show that an algebra admits a set of m near weight functions having a compatibility property, namely, the set is a “complete set”, if and only if it is the ring of regular functions of an affine geometrically irreducible algebraic curve defined over \({\mathbb{F}_q}\) whose points at infinity have a total of m rational branches. Then the codes produced using the near weight functions are exactly the AG codes supported on m points. A bound for the minimum distance of these codes is presented with examples which show that in some situations it compares better than the usual Goppa bound. 相似文献
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Zeying Wang 《组合设计杂志》2020,28(2):149-152
Partial difference sets with parameters are called Paley type partial difference sets. In this note, we prove that if there exists a Paley type partial difference set in an abelian group of order v, where v is not a prime power, then or , an odd integer. In 2010, Polhill constructed Paley type partial difference sets in abelian groups with those orders. Thus, combining with the constructions of Polhill and the classical Paley construction using nonzero squares of a finite field, we completely answer the following question: “For which odd positive integers , can we find a Paley type partial difference set in an abelian group of order ?” 相似文献
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Yutaka Hiramine 《Designs, Codes and Cryptography》2009,50(3):285-290
Let D be an affine difference set of order n in an abelian group G relative to a subgroup N. Set = H \ {1, ω}, where H = G/N and . Using D we define a two-to-one map g from to N. The map g satisfies g(σ
m
) = g(σ)
m
and g(σ) = g(σ
−1) for any multiplier m of D and any element σ ∈ . As applications, we present some results which give a restriction on the possible order n and the group theoretic structure of G/N.
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Work partially supported by a NATO Grant. 相似文献
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Indranil Biswas 《Archiv der Mathematik》2007,88(2):164-172
Let T be a complex torus and E
T
a holomorphic principal T-bundle over a connected complex manifold M. We prove that the total space of E
T
admits a K?hler structure if and only if M admits a K?hler structure and E
T
admits a flat holomorphic connection whose monodromy preserves a K?hler form on T. If E
T
admits a K?hler structure, then
is isomorphic to
.
Received: 2 September 2005 相似文献