Homogenization of binary linear codes and their applications

We introduce a new technique, called homogenization, for a systematic construction of augmented codes of binary linear codes, using the defining set approach in connection to multivariable functions. We explicitly determine the parameters and the weight distribution of the homogenized codes when the defining set is either a simplicial complex generated by any finite number of elements, or the difference of two simplicial complexes, each of which is generated by a single maximal element. Using this homogenization technique, we produce several infinite families of optimal codes, self-orthogonal codes, minimal codes, and self-complementary codes. As applications, we obtain some best known quantum errorcorrecting codes, infinite families of intersecting codes (used in the construction of covering arrays), and we compute the Trellis complexity (required for decoding) for several families of codes as well. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.