摘要：AbstractThe paper proposes to render the mathematic relations between the mathematic ideal of a generating polynomial from GF (2), the generating matrix of the type 4 x 7 associated to this ideal and the generating polynomial g(x), as well as the relations between the generating matrix H of the type 3 x 7, associated to a second mathematic ideal and to a second generating polynomial h(x). These generating polynomials as well as the generating matrixes G and H are not randomly selected, they being part of an associative general linear algebra generated by a polynomial f(x) from GF(2) that has as dividends the polynomials g(x) and h(x). All these we shall concretely exemplify in the proposed paper. Much more, we shall observe, also by a concrete example furnished in this paper, the connecting relations that exist between the matrixes G and H and that are very important in the mathematic theory of encodings. Practically, in the theory of encodings by redundant symbols, if between two matrixes there is no total relation of orthogonally, than the decoding cannot be realized. Therefore a property of the two matrixes is strictly necessary, this fact being also exemplified and demonstrated in this article.
