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1.
Stefka Buyuklieva 《Designs, Codes and Cryptography》1997,12(1):39-48
Methods to design binary self-dual codes with an automorphism of order two without fixed points are presented. New extremal self-dual [40,20,8], [42,21,8],[44,22,8] and [64,32,12] codes with previously not known weight enumerators are constructed. 相似文献
2.
Masaaki Harada 《Designs, Codes and Cryptography》2018,86(5):1085-1094
We give a classification of four-circulant singly even self-dual [60, 30, d] codes for \(d=10\) and 12. These codes are used to construct extremal singly even self-dual [60, 30, 12] codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. From extremal singly even self-dual [60, 30, 12] codes, we also construct optimal singly even self-dual [58, 29, 10] codes with weight enumerator for which no optimal singly even self-dual code was previously known to exist. Finally, we give some restriction on the possible weight enumerators of certain singly even self-dual codes with shadow of minimum weight 1. 相似文献
3.
J. E. Fields P. Gaborit W. C. Huffman V. Pless 《Designs, Codes and Cryptography》1999,18(1-3):125-148
Bachoc bachoc has recently introduced harmonic polynomials for binary codes. Computing these for extremal even formally self-dual codes of length 12, she found intersection numbers for such codes and showed that there are exactly three inequivalent [12,6,4] even formally self-dual codes, exactly one of which is self-dual. We prove a new theorem which gives a generator matrix for formally self-dual codes. Using the Bachoc polynomials we can obtain the intersection numbers for extremal even formally self-dual codes of length 14. These same numbers can also be obtained from the generator matrix. We show that there are precisely ten inequivalent [14,7,4] even formally self-dual codes, only one of which is self-dual. 相似文献
4.
In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodular lattices in dimension 40 are studied. We give a classification of extremal singly even self-dual codes of length 40. We also give a classification of extremal odd unimodular lattices in dimension 40 with shadows having 80 vectors of norm 2 through their relationships with extremal doubly even self-dual codes of length 40. 相似文献
5.
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
6.
The only example of a binary doubly-even self-dual [120,60,20] code was found in 2005 by Gaborit et al. (IEEE Trans Inform
theory 51, 402–407 2005). In this work we present 25 new binary doubly-even self-dual [120,60,20] codes having an automorphism of order
23. Moreover we list 7 self-dual [116,58,18] codes, 30 singly-even self-dual [96,48,16] codes and 20 extremal self-dual [92,46,16]
codes. All codes are new and present different weight enumerators.
相似文献
7.
In this note, we complete the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups. 相似文献
8.
A method for constructing binary self-dual codes having an automorphism of order p
2 for an odd prime p is presented in (S. Bouyuklieva et al. IEEE. Trans. Inform. Theory, 51, 3678–3686, 2005). Using this method, we investigate
the optimal self-dual codes of lengths 60 ≤ n ≤ 66 having an automorphism of order 9 with six 9-cycles, t cycles of length 3 and f fixed points. We classify all self-dual [60,30,12] and [62,31,12] codes possessing such an automorphism, and we construct
many doubly-even [64,32,12] and singly-even [66,33,12] codes. Some of the constructed codes of lengths 62 and 66 are with
weight enumerators for which the existence of codes was not known until now.
相似文献
9.
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
10.
《Finite Fields and Their Applications》2003,9(4):395-399
We find all extremal [76,38,14] binary self-dual codes having automorphism of order 19. There are three inequivalent such codes. One of them was previously known. The other two are new. These codes are the shortest known self-dual codes of minimal weight 14 as well as the best-known linear codes of that length and dimension. 相似文献
11.
Formally self-dual even codes have recently been studied. Double circulant even codes are a family of such codes and almost all known extremal formally self-dual even codes are of this form. In this paper, we classify all extremal double circulant formally self-dual even codes which are not self-dual. We also investigate the existence of near-extremal formally self-dual even codes. 相似文献
12.
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
13.
New extremal doubly-even [64, 32, 12] codes 总被引:1,自引:0,他引:1
In this paper, we consider a general construction of doubly-even self-dual codes. From three symmetric 2-(31, 10, 3) designs, we construct at least 3228 inequivalent extremal doubly-even [64, 32, 12] codes. These codes are distinguished by their K-matrices. 相似文献
14.
Masaaki Harada 《Designs, Codes and Cryptography》1996,8(3):273-283
Recently the author and Kimura have considered a construction of doubly-even codes from a given doubly-even code. In this note, we show that the restricutoion of doubly-even can be removed in the above construction. As an application, at least 137 inequivalent extremal doubly-even [56,28,12] codes and at least 1000 inequivalent extremal doubly-even [40,20,8] codes are constructed from known self-dual codes. The existence of new extremal singly-even codes is also described. 相似文献
15.
A complete classification is given of all [22, 11] and [24, 12] binary self-dual codes. For each code we give the order of its group, the number of codes equivalent to it, and its weight distribution. There is a unique [24, 12, 6] self-dual code. Several theorems on the enumeration of self-dual codes are used, including formulas for the number of such codes with minimum distance ? 4, and for the sum of the weight enumerators of all such codes of length n. Selforthogonal codes which are generated by code words of weight 4 are completely characterized. 相似文献
16.
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
17.
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
18.
All extremal binary self-dual [50,25,10] codes with an automorphism of order 7 are enumerated. Up to equivalence, there are four such codes, three with full automorphism group of order 21, and one code with full group of order 7. The minimum weight codewords yield quasi-symmetric 2-(49,9,6) designs.Research supported in part by NSA grant MDA904-95-H-1019. 相似文献
19.
Recently extremal double circulant self-dual codes have been classified for lengths n ≤ 62. In this paper, a complete classification
of extremal double circulant self-dual codes of lengths 64 to 72 is presented. Almost all of the extremal double circulant
singly-even codes given have weight enumerators for which extremal codes were not previously known to exist. 相似文献
20.
Ian McLoughlin 《Designs, Codes and Cryptography》2012,63(1):29-41
A new construction of the self-dual, doubly-even and extremal [48, 24, 12] binary linear block code is given. The construction
is much like that of a cyclic code from a polynomial. A zero divisor in a group ring with an underlying dihedral group generates
the code. A proof that the code is of minimum distance twelve, without need to resort to computation by computer, is outlined.
We also prove the code is self-dual, doubly even and that the code is an ideal in the group ring. The underlying group ring
structure is used, which offers a number of useful generator matrices for the code. Interestingly, the construction involves
unipotent elements within the group ring, and these lead to the creation of weighing matrices. 相似文献