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 class of doubly even self dual binary codes
โ Scribed by Jacques Wolfmann
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 268 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ 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.)
๐ SIMILAR VOLUMES
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.
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
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