  In this paper, we describe a correspondence between a fuzzy linear code and a
family of nested linear codes. We also describe the arithmetic of fuzzy linear
codes. As a special class of nested linear codes, we consider a family of
nested self-orthogonal codes. A linear code is self-orthogonal if it is
contained in its dual and self-dual if it is equal to its dual. We introduce a
definition of fuzzy self-dual or self-orthogonal codes which include classical
self-dual or self-orthogonal codes. As examples, we construct several
interesting classes of fuzzy linear codes including fuzzy Hamming codes, fuzzy
Golay codes, and fuzzy Reed-Muller codes. We also give a general decoding
algorithm for fuzzy linear codes.
