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1.
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
2.
Robin Chapman 《Finite Fields and Their Applications》1997,3(4):353-369
For certain primeslandp, and characters χ:F*p→F*l2, we construct codesWof lengthp+ 1 overFl2which are linear overFl, but not overFl2, and which are invariant under a monomial action of the group SL(2,p). We consider the cases of cubic and quartic characters in detail and use theWto construct linear codes overFlin these cases. 相似文献
3.
T. Aaron Gulliver Masaaki Harada Takuji Nishimura Patric R. J. Östergård 《Designs, Codes and Cryptography》2005,37(3):465-471
The weight enumerator of a formally self-dual even code is obtained by the Gleason theorem. Recently, Kim and Pless gave some
restrictions on the possible weight enumerators of near-extremal formally self-dual even codes of length divisible by eight.
In this paper, the weight enumerators for which there is a near-extremal formally self-dual even code are completely determined
for lengths 24 and 32, by constructing new near-extremal formally self-dual codes. We also give a classification of near-
extremal double circulant codes of lengths 24 and 32.
Communicated by: P. Fitzpatrick 相似文献
4.
In this paper, we investigate the covering radius of ternary extremal self-dual codes. The covering radii of all ternary extremal self-dual codes of lengths up to 20 were previously known. The complete coset weight distributions of the two inequivalent extremal self-dual codes of length 24 are determined. As a consequence, it is shown that every extremal ternary self-dual code of length up to 24 has covering radius which meets the Delsarte bound. The first example of a ternary extremal self-dual code with covering radius which does not meet the Delsarte bound is also found. It is worth mentioning that the found code is of length 32. 相似文献
5.
Rudolf Scharlau Pham Huu Tiep 《Transactions of the American Mathematical Society》1999,351(5):2101-2139
Let be an odd prime. It is known that the symplectic group has two (algebraically conjugate) irreducible representations of degree realized over , where . We study the integral lattices related to these representations for the case . (The case has been considered in a previous paper.) We show that the class of invariant lattices contains either unimodular or -modular lattices. These lattices are explicitly constructed and classified. Gram matrices of the lattices are given, using a discrete analogue of Maslov index.
6.
明平华 《数学的实践与认识》2004,34(6):159-161
由幂格的定义知 ,幂格与幂集格是不同的 ,然而它们却有一定的联系 .本文在幂格概念的基础上 ,进一步地讨论幂格和幂集格在一定条件下的联系 . 相似文献
7.
In this note, we give the complete classification of binary formally self-dual even codes of lengths 10, 12, 14 and 16. There are exactly fourteen, 29, 99 and 914 inequivalent such codes of lengths 10, 12, 14 and 16, respectively. This completes the classification of formally self-dual even codes of lengths up to 16. The first example of formally self-dual even code with a trivial automorphism group is also found. This shows that 16 is the smallest length for which there is a formally self-dual even code with a trivial automorphism group. 相似文献
8.
Masaaki Harada 《Discrete Mathematics》2017,340(10):2466-2468
In this note, we demonstrate that every binary doubly even self-dual code of length can be realized as the residue code of some extremal Type II -code. As a consequence, it is shown that there are at least inequivalent extremal Type II -codes of length . 相似文献
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10.
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
11.
明平华 《数学物理学报(A辑)》2004,24(4):491-495
该文在文[1]中幂格概念的基础上,得到了幂格的一个充要条件,给出了正则幂格、相对幂格的概念,并讨论了商格与正则幂格、相对幂格的关系.〖HT5”H〗关键词:〖HT5”SS〗格;幂格;商格;正则幂格;相对幂格. 相似文献
12.
G. Hughes 《Designs, Codes and Cryptography》2001,24(1):5-14
Using ideas from the cohomology of finite groups, an isomorphism is established between a group ring and the direct sum of twisted group rings. This gives a decomposition of a group ring code into twisted group ring codes. In the abelian case the twisted group ring codes are (multi-dimensional) constacyclic codes. We use the decomposition to prove that, with respect to the Euclidean inner product, there are no self-dual group ring codes when the group is the direct product of a 2-group and a group of odd order, and the ring is a field of odd characteristic or a certain modular ring. In particular, there are no self-dual abelian codes over the rings indicated. Extensions of these results to non-Euclidean inner products are briefly discussed. 相似文献
13.
14.
Pham Huu Tiep 《Geometriae Dedicata》1997,64(1):85-123
The notion of globally irreducible representations of finite groups has been introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell--Weil lattices of elliptic curves. In this paper we first give a necessary condition for global irreducibility. Then we classify all globally irreducible representations of L
2(q) and 2B2(q), and of the majority of the 26 sporadic finite simple groups. We also exhibit one more globally irreducible representation, which is related to the Weil representation of degree (pn-1)/2 of the symplectic group Sp2n(p) (p 1 (mod 4) is a prime). As a consequence, we get a new series of even unimodular lattices of rank 2(pn–1). A summary of currently known globally irreducible representations is given. 相似文献
15.
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
16.
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
17.
Steven T. Dougherty T. Aaron. Gulliver Manabu Oura 《Designs, Codes and Cryptography》2006,38(1):97-112
We study higher weights applied to ternary and quaternary self-dual codes. We give lower bounds on the second higher weight
and compute the second higher weights for optimal codes of length less than 24. We relate the joint weight enumerator with
the higher weight enumerator and use this relationship to produce Gleason theorems. Graded rings of the higher weight enumerators
are also determined.
This work was supported in part by Northern Advancement Center for Science & Technology and the Natural Sciences and Engineering
Research Council of Canada. 相似文献
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Five non-isomorphic quasi-symmetric 2-(49, 9, 6) designs are known. They arise from extremal self-dual [50, 25, 10] codes with a certain weight enumerator. Four of them have an automorphism of order 3 fixing two points. In this paper, it is shown that there are exactly 48 inequivalent extremal self-dual [50, 25, 10] code with this weight enumerator and an automorphism of order 3 fixing two points. 44 new quasi-symmetric 2-(49, 9, 6) designs with an automorphism of order 3 are constructed from these codes. 相似文献