Almost affine codes
Almost affine \(q\)-ary codes are codes having the property that puncturing in any set of positions results in a code for which the cardinality is a power of \(q\). The most obvious examples are cosets of linear codes. The matroid of an almost affine code is studied. An example is given of a matroid of an almost affine code that is not linearly representable. The connection between almost affine codes and perfect secret sharing schemes is given. It is reproved that binary and ternary almost affine codes are cosets of linear codes. The relation between an almost affine code and the dual of its matrix is explained, and results on the distance distribution and the dual distance distribution are obtained. Finally, the new concept of partial affine geometry is related to almost affine codes.
scientific article; zbMATH DE number 1164304
scientific article