Abstract:
It is necessary to encode data when transmitting over a noisy channel in order for
errors to be detected and corrected. List decoding algorithms provide all code words
within a specified distance of a received word in order to be sufficiently robust for
cases when two or more code words are equidistant from a received word. This paper
details a probabilistic method to obtain multiple close code words, motivated by list
decoding methods, for linear codes over fields of two or three elements. It employs a
variation on the LLL-Algorithm for lattice reduction that allows the LLL-Algorithm to
determine small elements in a vector space. Although it fails to return all code words
within a specified distance of a received word, the method is sufficiently robust to
provide some information if a received word is equidistant to multiple code words.
