PUB - Publikationen an der Universität Bielefeld

This paper continues the study of algebraic code capacities, which were introduced by Ahlswede (1971). He states an upper bound for the rates of codes which have the property that the code words form a linear space and the decoding procedure is arbitrary. It was asked (problem 5) whether this upper bound is actually the capacity if we deal with average errors. We answer this question in the affirmative for binary discrete memoryless channels. For nonbinary discrete memoryless channels we obtain slightly weaker result: If we allow those codes which have as code words a coset of a group which is a linear space, then the upper bound is again the capacity. An example shows that the result is not true for maximal error. In paragraph 3 we prove that the linear code capacity for compound channels with invariant transition probabilities equals the capacity for compound channels as given by Wolfowitz (1960).