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Two approaches to the extension problem for arbitrary weights over finite module alphabets

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Abstract

The extension problem underlies notions of code equivalence. Two approaches to the extension problem are described. One is a matrix approach that reduces the general problem for weights to one for symmetrized weight compositions. The other is a monoid algebra approach that reframes the extension problem in terms of modules over the monoid algebra determined by the multiplicative monoid of a finite ring.

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Acknowledgements

I thank Noha Abdelghany for a number of conversations that helped me clarify various ideas, such as Theorem 4.5. I thank the anonymous referees for catching several typos and suggesting some clarification in the proof of Proposition 5.4. I thank my wife Elizabeth S. Moore for her steadfast encouragement and support, especially while I was trying to prove Theorem 4.3. This paper is dedicated to the memory of our mothers.

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  1. Western Michigan University, 1903 W. Michigan Ave., Kalamazoo, MI, 49008-5248, USA

    Jay A. Wood

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  1. Jay A. Wood
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Correspondence to Jay A. Wood.

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In memoriam: Florence E. Wood, 1922–2019. Mary Elizabeth Keyte Moore, 1932–2019.

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Wood, J.A. Two approaches to the extension problem for arbitrary weights over finite module alphabets. AAECC 32, 427–455 (2021). https://doi.org/10.1007/s00200-020-00465-5

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  • DOI: https://doi.org/10.1007/s00200-020-00465-5

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