Minimum-change binary block-codes which are well balanced
In this paper, we deal with the following problem : how to code a counter (that is an interval of integers such as [0,n-1]) by the means of an adequate binary block-code so that each bit changes as few as possible when the counter runs the whole cycle and comes back to the first state ? This problem can be divided in two sub-ones. First, how to minimize the Hamming distance between two consecutives states of the counter ? Solutions of this problem have been known for a long time, as Gray codes. Second, how to spread the changed bits over the whole counter in a well balanced way ? The goal of this paper is to provide some solutions to the latter problem.
Such codes are useful in the case of wearing parts such as particular memory counters or input/output devices. In these cases it is requested to avoid that some places often change in the binary data, while some other places would rarely change (as in the case of natural binary coding). As a single example, we can think of some E2PROM set up in the most recent smart cards.
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