
For
An
This paper is a continuation of the work presented in [2], in which we described an algorithm for enumerating inequivalent binary self-dual codes. We used our algorithm to enumerate the self-dual codes of length up to and including 32. Our algorithm also found the size of the automorphism group of each code.
We have since made several improvements to our algorithm. It now generally runs faster. It also now finds generators for the automorphism group of each code. We have used our improved algorithm to enumerate the self-dual codes of length 34. We have also found the automorphism groups for each of our self-dual codes of length less than or equal to 34. The list of length 34 codes are new, as are the lists of automorphism groups for the length 32 and length 34 codes. We have found there are 19914 inequivalent length 34 codes with distance 4 and 938 length 34 codes with distance 6.
A graph is claw-free if it has no induced
A labeling
A three-fold Kirkman packing design
Let
We enumerate the self-orthogonal Latin squares of orders 1 through 9 and discuss the nature of the isomorphism classes of each order. Furthermore, we consider the possibility of enlarging sets of self-orthogonal Latin squares to produce complete sets.
A vertex-magic total labeling on a graph with
In this paper, we complete the classification of optimal binary linear self-orthogonal codes up to length 25. Optimal self-orthogonal codes are also classified for parameters up to length 40 and dimension 10. The results were obtained via two independent computer searches.
In this paper we examine the classical Williamson construction for Hadamard matrices, from the point of view of a striking analogy with isomorphisms of division algebras. By interpreting the 4 Williamson array as a matrix arising from the real quaternion division algebra, we construct Williamson arrays with 8 matrices, based on the real octonion division algebra. Using a Computational Algebra formalism we perform exhaustive searches for even-order 4-Williamson matrices up to 18 and odd- and even-order 8-Williamson matrices up to 9 and partial searches for even-order 4-Williamson matrices up to 22 and odd- and even-order 8-Williamson matrices for orders 10 — 13. Using Magma, we conduct searches for inequivalent Hadamard matrices within all the sets of matrices obtained by exhaustive and partial searches. In particular, we establish constructively ten new lower bounds for the number of inequivalent, Hadamard matrices of the consecutive orders 72, 76, 80, 84, 88, 92, 96, 100, 104 and 108.
This article continues the study of a class of non-terminating expansions of sin
The work, which has a historical backdrop to it, is discussed in the context of prior results by the author and others.
1970-2025 CP (Manitoba, Canada) unless otherwise stated.