Abstract
Abstract : The optimum quadratic (15,8) code with minimum distance d=5, recently discovered and studied by Nordstrom and Robinson, can be rather naturally described in terms of polynomials over GF(2). It is shown that the Nordstrom- Robinson code consists of a linear code and of a certain subset of its cosets, which account for its non-linear nature. This representation leads to a non- heuristic proof that weight and distance structures can be treated analogously and that the minimum distance and weight are 5. The analysis of this mechanism may be an essential step in the discovery of an entire class of non-linear double error correcting codes. The given analysis also suggests a systematic decoding procedure. This is based on permutations which map any correctable error pattern (double or single errors) into digit positions for which the computation of a syndrome allows the correction. The correct code word can then be recovered through the inverse permutation.
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