Ternary maximal self-orthogonal codes of lengths 21,2221,22 and 2323

We give a classification of ternary maximal self-orthogonal codes of lengths $21,22$ and $23$. This completes a classification of ternary maximal self-orthogonal codes of lengths up to $24$

The codes and the lattices of Hadamard matrices

It has been observed by Assmus and Key as a result of the complete classification of Hadamard matrices of order 24, that the extremality of the binary code of a Hadamard matrix H of order 24 is equivalent to the extremality of the ternary code of H^T. In this note, we present two proofs of this fact, neither of which depends on the classification. One is a consequence of a more general result on the minimum weight of the dual of the code of a Hadamard matrix. The other relates the lattices obtained from the binary code and from the ternary code. Both proofs are presented in greater generality to include higher orders. In particular, the latter method is also used to show the equivalence of (i) the extremality of the ternary code, (ii) the extremality of the Z_4-code, and (iii) the extremality of a lattice obtained from a Hadamard matrix of order 48.Comment: 16 pages. minor revisio

Hadamard Matrices of Orders 60 and 64 with Automorphisms of Orders 29 and 31

A classification of Hadamard matrices of order 2p + 2 with an automorphism of order p is given for p = 29 and 31. The ternary self-dual codes spanned by the newly found Hadamard matrices of order 60 with an automorphism of order 29 are computed, as well as the binary doubly even self-dual codes of length 120 with generator matrices defined by related Hadamard designs. Several new ternary near-extremal self-dual codes, as well as binary near-extremal doubly even self-dual codes with previously unknown weight enumerators are found

A gluing technique for constructing relatively self-dual codes

AbstractIn this paper, we introduce self-dual codes relative to certain symmetric bilinear forms over a finite commutative ring. By refining the gluing theory of Conway, Pless, and Sloane, we obtain a gluing technique for constructing relatively self-dual codes. As examples of application of our technique, we find a construction of a self-dual binary [2(m + 3), m + 3, 6]-code from a self-dual [2m, m, l]-code with l⩾6, and a construction of doubly-even binary self-dual [2(m + 4), m + 4, 8]-code from a doubly even self-dual [2m, m, t]-code with t ⩾ 8

Self-Dual Codes

Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration, extremal codes, open problems. There is a comprehensive bibliography.Comment: 136 page