87 research outputs found
On extremal self-dual ternary codes of length 48
All extremal ternary codes of length 48 that have some automorphism of prime
order are equivalent to one of the two known codes, the Pless code or
the extended quadratic residue code
Some MDS Codes over Gf(64) Connected with the Binary Doubly-Even [72,36,16] Code
* The author is supported by a Return Fellowship from the Alexander von Humboldt
Foundation.MDS [8,4,5] codes over a field with 64 elements are constructed.
All such codes which are self-dual under a Hermitian type inner product are
classified. The connection between these codes and a putative binary self-
dual [72,36,16] code is considered
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
On the Structure of the Linear Codes with a Given Automorphism
The purpose of this paper is to present the structure of the linear codes
over a finite field with q elements that have a permutation automorphism of
order m. These codes can be considered as generalized quasi-cyclic codes.
Quasi-cyclic codes and almost quasi-cyclic codes are discussed in detail,
presenting necessary and sufficient conditions for which linear codes with such
an automorphism are self-orthogonal, self-dual, or linear complementary dual
The extremal codes of length 42 with automorphism of order 7
AbstractAll [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 orders 60 and 64 with automorphisms of orders 29 and 31
A classification of Hadamard matrices of order with an automorphism of
order is given for and . The ternary self-dual codes spanned by
the newly found Hadamard matrices of order with an automorphism of order
are computed, as well as the binary doubly even self-dual codes of length
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.Comment: 21 page
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