Extension Theorems for Linear Codes over Finite Rings
Extension Theorems for Linear Codes over Finite Rings
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DOI：
10.1007/3-540-63163-1_26
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发表时间：
1997-06
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影响因子：
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通讯作者：
Jay A. Wood
中科院分区：
文献类型：
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作者：
Jay A. Wood
讨论了有限环上线性码的扩张问题的各种形式。证明了有限Frobenius环上对称权合成的扩张定理。作为结果，还证明了有限交换环上权函数的一个扩张定理。证明利用线性独立的字符，以及线性独立的字符平均轨道上的一组行动。
Various forms of the extension problem are discussed for linear codes defined over finite rings. The extension theorem for symmetrized weight compositions over finite Frobenius rings is proved. As a consequence, an extension theorem for weight functions over certain finite 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.