Extension Theorems for Linear Codes over Finite Rings
نویسنده
چکیده
Various forms of the extension problem are discussed for linear codes de ned over nite rings. The extension theorem for symmetrized weight compositions over nite Frobenius rings is proved. As a consequence, an extension theorem for weight functions over certain nite commutative rings is also proved. The proofs make use of the linear independence of characters as well as the linear independence of characters averaged over the orbits of a group action.
منابع مشابه
MacWilliams Extension Theorems and the Local-Global Property for Codes over Rings
The MacWilliams extension theorem is investigated for various weight functions over finite Frobenius rings. The problem is reformulated in terms of a local-global property for subgroups of the general linear group. Among other things, it is shown that the extension theorem holds true for poset weights if and only if the underlying poset is hierarchical. Specifically, the Rosenbloom-Tsfasman wei...
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