In this paper, two general methods for constructing self-dual codes are presented. These methods use circulant matrices in circulant or bordered circulant structures to construct the suitable generator matrices. The necessary and sufficient conditions, for the generated codes to be self-dual, are provided. Special cases of the proposed methods include the well known "Pure Double Circulant" construction and the "Bordered Double circulant" construction of self-dual codes. As an example, the methods were applied to search for self-dual codes in G F(5). Many new inequivalent self-dual codes with best known distance are found.

Orthogonal arrays, Isomorphism, Construction algorithm,

We give an algorithm to obtain formulae and values for minors of Hadamard matrices. One step in our algorithm allows the (n-j) x (n-j) minors of an Hadamard matrix to be given in terms of the minors of a 2j-1 x 2j-1 matrix. In particular we illustrate our algorithm by finding explicitly all the (n-4) x (n-4) minors of an Hadamard matrix.

Orthogonal arrays, Isomorphism, Construction algorithm, Projection properties, Primary 62K15, Secondary 05B20,

No abstract