منابع مشابه
On self-dual doubly-even extremal codes
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 following, an extremal code means a binary linear self-dual doubly-even extremal code. We use the set-the...
متن کاملOn the performance of optimal double circulant even codes
In this note, we investigate the performance of optimal double circulant even codes which are not self-dual, as measured by the decoding error probability in bounded distance decoding. To do this, we classify the optimal double circulant even codes that are not self-dual which have the smallest weight distribution for lengths up to 72. We also give some restrictions on the weight enumerators of...
متن کاملCodes from Hall planes of even order
We show that the binary code C of the projective Hall plane Hq2 of even order q where q = 2, for t ≥ 2 has words of weight 2q in its hull that are not the difference of the incidence vectors of two lines of Hq2 ; together with an earlier result for the dual Hall planes of even order, this shows that for all t ≥ 2 the Hall plane and its dual are not tame. We also deduce that dim(C) > 3+1, the di...
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We determine the structure of cyclic codes over Z4 for arbitrary even length giving the generator polynomial for these codes. We determine the number of cyclic codes for a given length. We describe the duals of the cyclic codes, describe the form of cyclic codes that are self-dual and give the number of these codes. We end by examining specific cases of cyclic codes, giving all cyclic self-dual...
متن کاملBinary codes of the symplectic generalized quadrangle of even order
Let q be a prime power and W (q) be the symplectic generalized quadrangle of order q. For q even, let O (respectively, E , T ) be the binary linear code spanned by the ovoids (respectively, elliptic ovoids, Tits ovoids) of W (q) and Γ be the graph defined on the set of ovoids ofW (q) in which two ovoids are adjacent if they intersect at one point. For A ∈ {E , T ,O}, we describe the codewords o...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90410-4