Research to develop the algebraic theory of codes
Abstract
Abstract : A new bound on minimum distance for a class of cyclic codes of type (3p,p) is found. For p = 29 this and a small computer search yield new 5-designs on 30 points. Automorphism groups of quadratic-residue codes are discussed, and the orbit-structure of PSL2(47) on minimum-weight vectors of such a code is determined. Some graphs related to codes are discussed, and some bounds on Ramsey numbers are obtained. Some remarks on the covering radius and a decoding method are presented. The existence of good codes in a small class of codes is proved, and a class of optimal cyclic codes is constructed. Some comments on the literature are made. (Author)
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