Finite field and group algorithms for orthogonal sequence search

Introduction: Hadamard matrices consisting of elements 1 and –1 are an ideal object for a visual application finite dimensional mathematics operating with number addresses elements. The notation systems abstract algebra methods, in contrast to the conventional matrix algebra, have been changing intensively, without being widely spread, leading necessity revise systematize accumulated experience. Purpose: To describe algorithms fields groups uniform order facilitate perception extensive knowledge necessary finding orthogonal suborthogonal sequences. Results: Formulas proposed calculating relatively unknown (or their versions) developed by Scarpis, Singer, Szekeres, Goethal — Seidel, Noboru Ito, as well polynomial equations used prove theorems about existence finite-dimensional solutions. This replenished significant lack information both domestic literature (most these issues published here first time) abroad. Practical relevance: Orthogonal sequences methods effective via theory direct practical importance noise-immune coding, compression masking video data.