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A class of doubly even self dual binary codes

โœ Scribed by Jacques Wolfmann


Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
268 KB
Volume
56
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


We give a construction of an infinite class of doubly even self dual binary codes including a code of length 112. (The study of such a code is closely related to the existence problem of a projective plane of order ten.)


๐Ÿ“œ SIMILAR VOLUMES


On self-dual doubly-even extremal codes
โœ Helmut Koch ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 488 KB

Let C be a binary linear self-dual doubly-even code of length n and minimal weight d. Such codes exist only if 12 = 0 (mod 8). We put II = 24r + 8s, s = 0, 1, 2. It follows from the work of Gleason [2] and of Mallows and Sloane [6] that d s 4r + 4. C is called extremal if d = 4r + 4. In the followin

A group algebra construction of binary e
โœ J Wolfmann ๐Ÿ“‚ Article ๐Ÿ“… 1987 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 504 KB

We give a construction of binary doubly even self dual codes as binary images of some principal ideals in a group algebra. In particular, we show how to produce such a code starting from any binary cyclic code with length not a multiple of 4 and dimension at least 3.

The Existence of a Self-Dual [70, 35, 12
โœ Masaaki Harada ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 224 KB

In this note, the existence of self-dual codes and formally self-dual even codes is investigated. A construction for self-dual codes is presented, based on extending generator matrices. Using this method, a singly-even self-dual [70, 35, code is constructed from a self-dual code of length 68. This i

The [52, 26, 10] Binary Self-Dual Codes
โœ W.Cary Huffman; Vladimir D. Tonchev ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 229 KB

All [52, 26,10] binary self-dual codes with an automorphism of order 7 are enumerated. Up to equivalence, there are 499 such codes. They have two possible weight enumerators, one of which has not previously arisen. 2001 Academic Press 1. INTRODUCTION In [1], Conway and Sloane present an upper bound