Self-Testing Embedded Borden t-UED Code Checkers for t = 2kq − 1 with q = 2m − 1

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Abstract

Borden codes are optimal nonsystematic t-unidirectional error detecting (t-UED) codes. A possible method to design a Borden code checker is to map the Borden code words to words of an AN arithmetic code and to check the obtained words with an appropriate AN code checker. For t = q − 1 with q = 2m − 1 we show how this method can be modified such that the Borden code checkers achieve the self-testing property under very weak conditions. It is only required that no checker input line gets a constant signal and that the Borden code words occur in a random order, making the proposed checkers very suitable for use as embedded checkers. Based on these checkers it is then possible to design embedded Borden t-UED code checkers for t = 2kq − 1 with q = 2m − 1.

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