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# mossmann / unambiguous-encapsulation

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 Isolated Complementary Binary Linear Block Codes ICBLBCs are binary linear block codes composed of sub-codes that feature isolation from each other. A binary linear block code encodes a certain number of data bits into a codeword of a certain length. A codeword of n bits uniquely represents a block of k data bits. Binary linear block codes are often characterized by the minimum Hamming distance d between any two codewords. A sub-code is a code that consists of a subset of the codewords of a larger code. Complementary codes are non-overlapping sub-codes of the same larger code. An ICBLBC is a set of two or more complementary codes that feature isolation from each other. Isolation means that there is a minimum Hamming distance from sub-code to sub-code. For isolation to be useful for unambiguous encapsulation, it must be larger than the minimum Hamming distance within each sub-code. This project seeks ICBLBCs consisting of only two sub-codes. Definitions The terms "Isolated Complementary Binary Linear Block Code", "ICBLBC", "complementary", "sub-code", and "isolation" as used in this description are my own. These terms are subject to change upon review of this description by members of the coding theory community. Example The following ICBLBC contains a total of eight codewords divided into two sub-codes of four codewords each: - 00000, 00011, 00101, 01001 - 01110, 10110, 11010, 11100 Each codeword is five bits long (n = 5). Within each sub-code, each codeword represents two data bits (k = 2). Considering the ICBLBC as a whole, each codeword represents three data bits (k = 3). The minimum Hamming distance within each sub-code is two. The minimum Hamming distance from one sub-code to the other (the isolation) is three.