Combinatorial polarization, code loops, and codes of high level

Details Combinatorial polarization, code loops, and codes of high level Combinatorial polarization, code loops, and codes of high level

2007-01-24

arxiv.org/abs/math/0701708v1

proceedings of CombinaTexas 2003, published in International Journal of Mathematics and Mathematical Sciences 29 (2004), 1533-

Mathematics

Group Theory

9 pages

Scientific paper

We first find the combinatorial degree of any map $f:V\to F$ where $F$ is a finite field and $V$ is a finite-dimensional vector space over $F$. We then simplify and generalize a certain construction due to Chein and Goodaire that was used in characterizing code loops as finite Moufang loops that posses at most two squares. The construction yields binary codes of high divisibility level with prescribed Hamming weights of intersections of codewords.

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