الفهرس 
Codes over finite modules
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Abstract
In this thesis, we revisit MacWilliams{u2019} classical results for codes over{uFB01}nite {uFB01}elds. The {uFB01}rst result is the MacWilliams identities. We study theseidentities in the classical setting and their generalizations to codes over {uFB01}nite rings and modules. The second result is the MacWilliams extension theorem, which states that two codes are isometric if and only if they aremonomially equivalent. MacWilliams proved this theorem in the 1960{u2019}s for codes over {uFB01}nite {uFB01}elds with respect to the Hamming weight. We study this theorem and how it was generalized to codes over {uFB01}nite rings and codes over {uFB01}nite modules, as well as to various weight functions. The main result of thethesis is proving a su{uFB03}cient condition for a module alphabet A to satisfy the extension property with respect to symmetrized weight compositions. Fi-nally, we introduce exotic isometries and give examples of this phenomenon