Abstract
We will say that an alphabet A satisfies the extension property with respect to a weight w if every linear isomorphism between two linear codes in A n that preserves w extends to a monomial transformation of A n. In the 1960s MacWilliams proved that finite fields have the extension property with respect to Hamming weight. It is known that a module A has the extension property with respect to Hamming weight or a homogeneous weight if and only if A is pseudo-injective and embeds into \(\hat{R}\). The main theorem presented in this paper gives a sufficient condition for an alphabet to have the extension property with respect to symmetrized weight compositions. It has already been proven that a Frobenius bimodule has the extension property with respect to symmetrized weight compositions. This result follows from the main theorem.
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ElGarem, N., Megahed, N., Wood, J.A. (2015). The Extension Theorem with Respect to Symmetrized Weight Compositions. In: Pinto, R., Rocha Malonek, P., Vettori, P. (eds) Coding Theory and Applications. CIM Series in Mathematical Sciences, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-17296-5_18
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DOI: https://doi.org/10.1007/978-3-319-17296-5_18
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