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Let Ax = B be a system of m x n linear equations with integer coefficients. Assume the rows of A are linearly independent and denote by X (respectively Y) the maximum of the absolute values of the m x m minors of the matrix A (the augmented matrix (A, B)). If the system has a solution in nonnegative integers, it is proved that the system has a solution X =… (More)

Blakley and Borosh introduced a general theory of codes, encompassing cryptographic and error control codes among others. They explored the properties of such general codes with methods from rela-tional algebra and set theory. We provide a categorical point of view, which leads to new constructions of codes. We also exhibit a Jordan-Hölder type theorem and… (More)

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