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1.
In this paper, we study binary optimal odd formallyself-dual codes. All optimal odd formally self-dual codes areclassified for length up to 16. The highest minimum weight ofany odd formally self-dual codes of length up to 24 is determined. We also show that there is a unique linearcode for parameters [16, 8, 5] and [22, 11, 7], up to equivalence. 相似文献
2.
In this paper we discuss the security of digital signature schemes based on error-correcting codes. Several attacks to the Xinmei scheme are surveyed, and some reasons given to explain why the Xinmei scheme failed, such as the linearity of the signature and the redundancy of public keys. Another weakness is found in the Alabbadi-Wicker scheme, which results in a universal forgery attack against it. This attack shows that the Alabbadi-Wicker scheme fails to implement the necessary property of a digital signature scheme: it is infeasible to find a false signature algorithm D
from the public verification algorithm E such that E(D
(
)) =
for all messages
. Further analysis shows that this new weakness also applies to the Xinmei scheme. 相似文献
3.
Combinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established using orthogonal designs. This method has led to the construction of many new self-dual codes over small finite fields and rings. In this paper, we generalize this method by using generalized orthogonal designs, and we give another new method that creates and solves Diophantine equations over GF(p) in order to find suitable generator matrices for self-dual codes. We show that under the necessary conditions these methods can be applied as well to small and large fields. We apply these two methods to study self-dual codes over GF(31) and GF(37). Using these methods we obtain some new maximum distance separable self-dual codes of small orders. 相似文献
4.
Let F_q be a finite field with q = p~m, where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length 2~ap~r over F_q, a ≥ 1.The construction of self-dual negacyclic codes of length 2~abp~r over F_q is also provided, where gcd(2, b) = gcd(b, p) = 1 and a ≥ 1. 相似文献
5.
《Applied Mathematics Letters》2000,13(2):17-19
Let [n, k, d; q]-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). Let d8(n, k) be the maximum possible minimum Hamming distance of a linear [n, k, d; 8]-code for given values of n and k. In this paper, eighteen new linear codes over GF(8) are constructed which improve the table of d8(n, k) by Brouwer. 相似文献
6.
Keisuke Shiromoto 《Designs, Codes and Cryptography》1999,16(1):87-92
We have the relationships between the Hamming weight enumerator of linear codes over GFq
m which have generator matrices over GFq, the support weight enumerator and the -ply weight enumerator. 相似文献
7.
In this paper it is shown that the weight enumerator of a bordered double circulant self-dual code can be obtained from those of a pure double circulant self-dual code and its shadow through a relationship between bordered and pure double circulant codes. As applications, a restriction on the weight enumerators of some extremal double circulant codes is determined and a uniqueness proof of extremal double circulant self-dual codes of length 46 is given. New extremal singly-even [44,22,8] double circulant codes are constructed. These codes have weight enumerators for which extremal codes were not previously known to exist. 相似文献
8.
Steven T. Dougherty T. Aaron Gulliver Masaaki Harada 《Journal of Algebraic Combinatorics》1999,9(3):233-250
In this paper, we investigate self-dual codes over finite rings, specifically the ring
of integers modulo 2m. Type II codes over
are introduced as self-dual codes with Euclidean weights which are a multiple of 2m +1. We describe a relationship between Type II codes and even unimodular lattices. This relationship provides much information on Type II codes. Double circulant Type II codes over
are also studied. 相似文献
9.
10.
All singly-even self-dual [40,20,8] binary codes which have an automorphism of prime order
are obtained up to equivalence. There are two inequivalent codes with an automorphism of order 7 and 37 inequivalent codes with an automorphism of order 5. These codes have highest possible minimal distance and some of them are the first known codes with weight enumerators prescribed by Conway and Sloane. 相似文献
11.
Noboru Ito 《Journal of Combinatorial Theory, Series A》1980,29(2):251-253
A lower bound is given for the minimum weight of the symmetry code C(q) over GF(3), which is introduced by Pless [3]. 相似文献
12.
13.
14.
Torleiv Kløve 《Discrete Mathematics》1978,23(2):159-168
We study the weight distribution of the linear codes over GF(ql) which have generator matrices over GF(q) and their dual codes. As an application we find the weight distribution of the irreducible cyclic (23(21≈1), 111) codes over GF(2) for all lnot divisible by 11. 相似文献
15.
In a fundamental paper on the algebraic theory of graph colouring Tutte [2] proves that the only tangential 1-block over GF(2) is the geometry corresponding to the polygon matroid of the graph K3. For a good discussion of the problem and a direct proof of Tutte's theorem see Aigner [1, p. 373].
The purpose of this note is to prove the following result. 相似文献
16.
Toyoharu Itoh 《Geometriae Dedicata》1998,69(3):261-286
Given a 2-(l,3,q3(ql-5-1/q-1);q) design for an integer l 5 mod 6(q-1) which admits the action of a Singer cycle Zl of GLl(q), we construct a 2-(ml,3,q3(ql-5-1/q-1);q) design for an arbitrary integer m 3 which admits the action of SLm(ql). The construction applied to Suzuki's designs actually provides a new family of 2-designs over GF(q) which admit the SLm(ql) action. 相似文献
17.
In this article we outline a computer assisted classification of the ovoids in an orthogonal space of the type .
18.
19.
Masaaki Harada 《Designs, Codes and Cryptography》2006,38(1):5-16
In this paper, we show that the code generated by the rows of a block-point incidence matrix of a self-orthogonal 3-(56,12,65)
design is a doubly-even self-dual code of length 56. As a consequence, it is shown that an extremal doubly-even self-dual
code of length 56 is generated by the codewords of minimum weight. We also demonstrate that there are more than one thousand
inequivalent extremal doubly-even self-dual [56,28,12] codes. This result shows that there are more than one thousand non-isomorphic
self-orthogonal 3-(56,12,65) designs.
AMS Classification: 94B05, 05B05 相似文献
20.
In this paper, a construction of ternary self-dual codes based on negacirculant matrices is given. As an application, we construct
new extremal ternary self-dual codes of lengths 32, 40, 44, 52 and 56. Our approach regenerates all the known extremal self-dual
codes of lengths 36, 48, 52 and 64. New extremal ternary quasi-twisted self-dual codes are also constructed.
Supported by an NSERC discovery grant and a RTI grant.
Supported by an NSERC discovery grant and a RTI grant.
A summer student Chinook Scholarship is greatly appreciated. 相似文献