Orthogonal Latin Square Codes

Abstract

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 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> data bits, where m is an integer, and 2tm check bits for t-error correcting.