Abstract
Let \(\texttt {R}\) be a finite commutative Frobenius ring and \(\texttt {S}\) a Galois extension of \(\texttt {R}\) of degree m. For positive integers k and \(k'\), we determine the number of free \(\texttt {S}\)-submodules \(\mathcal {B}\) of \(\texttt {S}^\ell \) with the property \(k=\texttt {rank}_\texttt {S}(\mathcal {B})\) and \(k'=\texttt {rank}_\texttt {R}(\mathcal {B}\cap \texttt {R}^\ell )\). This corrects the wrong result (Bill in Linear Algebr Appl 22:223–233, 1978, Theorem 6) which was given in the language of codes over finite fields.
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Partially funded by MINECO MTM2015-65764-C3-1-P and MTM2015-69138-REDT Grants.
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Communicated by J. D. Key.
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Bandi, R., Tabue, A.F. & Martínez-Moro, E. On counting subring-submodules of free modules over finite commutative frobenius rings. Des. Codes Cryptogr. 86, 2247–2254 (2018). https://doi.org/10.1007/s10623-017-0446-1
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DOI: https://doi.org/10.1007/s10623-017-0446-1