Title: Isometries of Codes

 

Abstract: A code is endowed with the Hamming distance, which in turn determines its error-correcting capabilities. This suggests the study of isometries between codes. In 1961, MacWilliams with her famous Extension Theorem, classified Hamming isometries of linear codes over finite fields. This result was generalized for different weight functions, different alphabets and recently, for sublinear codes. We discuss the extension theorems for isometries of codes in their full generality and generalize some existing results.