A new class of multiple-error correcting codes has been developed. Since it belongs to the class of one-step-decodable majority codes, it can be decoded at an exceptionally high speed. This class of codes is derived from a set of mutually orthogonal Latin squares. This mutually orthogonal property provides a class of codes having a unique feature of “modularity.” The parity check matrix possesses a uniform pattern and results in a small number of inputs to modulo 2 adders. This class of codes has m2data bits, where m is an integer, and 2tm check bits for t-error correcting.
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Hsiao et al. (1970) studied this question.
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