On the classification of the extremal self-dual codes over small fields with 2-transitive automorphism groups

There are seven binary extremal self-dual doubly-even codes which are known to have a 2-transitive automorphism group. Using representation theoretical methods we show that there are no other such codes, except possibly for length n = 1024. We also classify all extremal ternary self-dual and quaternary Hermitian self-dual codes.     

On the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups

In this note, we complete the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups.     

The extremal codes of lengths 76 with an automorphism of order 19

We find all extremal [76,38,14] binary self-dual codes having automorphism of order 19. There are three inequivalent such codes. One of them was previously known. The other two are new. These codes are the shortest known self-dual codes of minimal weight 14 as well as the best-known linear codes of that length and dimension.     

ContributionsThe extremal codes of length 42 with automorphism of order 7

All [42, 21, 8] binary self-dual codes with automorphisms of order 7 are enumerated. Up to equivalence there are 16 such codes. These codes are defined with their generator matrices.     

Hadamard matrices of order 32 and extremal ternary self-dual codes

A ternary self-dual code can be constructed from a Hadamard matrix of order congruent to 8 modulo 12. In this paper, we show that the Paley–Hadamard matrix is the only Hadamard matrix of order 32 which gives an extremal self-dual code of length 64. This gives a coding theoretic characterization of the Paley–Hadamard matrix of order 32.     

On Hadamard matrices of order 2(p+1) with an automorphism of odd prime order p

In this paper, we investigate Hadamard matrices of order 2(p + 1) with an automorphism of odd prime order p. In particular, the classification of such Hadamard matrices for the cases p = 19 and 23 is given. Self‐dual codes related to such Hadamard matrices are also investigated. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 367–380, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10052