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3.2. Combinatorial Solutions: Exhaustive Search and Birthday Decoding

In this session, I will detail two combinatorial solutions to the decoding problem. The first one is the Exhaustive Search. To find our w columns, we will simply enumerate all the tuples j1 to jw and check whether the corresponding column plus the syndrome is equal to zero modulo 2. In detail here is how we will do. We have w loops enumerating the indices from j1 to jw, and in the innermost loop, we add the w columns plus the syndrome and either we test the value of the syndrome or ...
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