Substitution of characters in q-ary m-sequences
This paper discusses a simple way of increasing the linear complexity of maximal length q-ary sequences. This is attained by using character substitution tables. The achievable maximum of increase is determined and it is shown that a portion of about 1/e of all substitution tables share this maximum. The mean value and the variance of the linear complexity is derived for the sequence's output by randomly chosen substitutions. The special case of permutations as substitutions are investigated, as well. At the end of the paper we propose an extension of the notion of linear complexity.
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