Isometries of Additive Codes
نویسندگان
چکیده
(June 15, 2016.) FIX: June 15, 2016. This needs to be re-written. Monomial transformations of linear codes are linear isometries for the Hamming weight. A code alphabet has the extension property for the Hamming weight when every linear isometry between codes extends to a monomial transformation. MacWilliams proved that finite fields have the extension property for the Hamming weight. In contrast, additive codes over F4 do not have the extension property for the Hamming weight. When a code alphabet does not satisfy the extension property, the monomial automorphisms of a code may differ from its isometries. The main theorem proves there exist codes where the difference can be as arbitrary as possible.
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