Classes of self-orthogonal or self-dual codes from orbit matrices of Menon designs

Orthogonal designs and MDS self-dual codes

Construction of MDS self-dual codes from orthogonal matrices

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.

Symmetric Designs and Self-dual Codes

A construction is given for associating to any symmetric (v, k, X) design a self-dual code of length v+ 1 over GF (p), where p is any divisor of the square-free part of k — k. These codes are then used to obtain a substantial strengthening of a result of Hughes on automorphisms of designs. Specifically, suppose a symmetric {v, k, X) design possesses an automorphism a of odd prime order q. If an...

Orthogonal, Antiorthogonal and Self-Orthogonal Matrices and their Codes

Orthogonal matrices over arbitrary elds are de ned together with their non-square analogs, which are termed row-orthogonal matrices. Antiorthogonal and self-orthogonal square matrices are introduced together with their non-square analogs. The relationships of these matrices to such codes as self-dual codes and linear codes with complementary duals are given. These relationships are used to obta...

Self-dual and maximal self-orthogonal codes over F7

In this note, we give the classi5cation of self-dual F7-codes of length 12 and maximal self-orthogonal codes of lengths 10; 11 and 13. It is also shown that there is no self-dual [16; 8; d¿ 8] code over F7. c © 2002 Elsevier Science B.V. All rights reserved.