An Algorithmic Reduction Theory for Binary Codes: LLL and more

In this article, we propose an adaptation of the algorithmic reduction theory lattices to binary codes. This includes celebrated LLL algorithm (Lenstra, Lenstra, Lovasz, 1982), as well adaptations associated algorithms such Nearest Plane Algorithm Babai (1986). Interestingly, codes can be interpreted version bound Griesmer (1960) on minimal distance a code. Using these algorithms, demonstrate—both with heuristic analysis and in practice—a small polynomial speed-up over Information-Set Decoding Lee Brickell (1988) for random appears first that is not based time-memory trade-off. The above should read very preliminary example potential codes, cryptanalysis.