Abstract
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.
Partially supported by NSA grants MDA904-94-H-2025 and MDA904-96-1-0067, and by Purdue University Calumet Scholarly Research Awards.
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Wood, J.A. (1997). Extension theorems for linear codes over finite rings. In: Mora, T., Mattson, H. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1997. Lecture Notes in Computer Science, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63163-1_26
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DOI: https://doi.org/10.1007/3-540-63163-1_26
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