2019
DOI: 10.1109/tit.2018.2889244
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On the Maximum Size of Block Codes Subject to a Distance Criterion

Abstract: We establish a general formula for the maximum size of finite length block codes with minimum pairwise distance no less than d. The achievability argument involves an iterative construction of a set of radius-d balls, each centered at a codeword. We demonstrate that the number of such balls that cover the entire code alphabet cannot exceed this maximum size. Our approach can be applied to codes i) with elements over arbitrary code alphabets, and ii) under a broad class of distance measures, thereby ensuring th… Show more

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