Orthogonality Matrices for Modules over Finite Frobenius Rings and MacWilliams' Equivalence Theorem
نویسندگان
چکیده
منابع مشابه
MacWilliams type identities for some new $m$-spotty weight enumerators over finite commutative Frobenius rings
Past few years have seen an extensive use of RAM chips with wide I/O data (e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly vulnerable to a special type of byte error, called an m-spotty byte error, which can be effectively detected or corrected using byte errorcontrol codes. The MacWilliams identity provides the relationship between the weight distribution of a code and...
متن کاملMacWilliams Type identities for $m$-spotty Rosenbloom-Tsfasman weight enumerators over finite commutative Frobenius rings
The m-spotty byte error control codes provide a good source for detecting and correcting errors in semiconductor memory systems using high density RAM chips with wide I/O data (e.g. 8, 16, or 32 bits). m-spotty byte error control codes are very suitable for burst correction. M. Özen and V. Siap [7] proved a MacWilliams identity for the m-spotty Rosenbloom-Tsfasman (shortly RT) weight enumerator...
متن کاملCode Equivalence Characterizes Finite Frobenius Rings
In this paper we show that finite rings for which the code equivalence theorem of MacWilliams is valid for Hamming weight must necessarily be Frobenius. This result makes use of a strategy of Dinh and López-Permouth.
متن کاملOrthogonality Matrices for Modulesover Finite Frobenius RingsandMacWilliams’ EquivalenceTheorem
MacWilliams’ equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control 37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in orde...
متن کاملOn nest modules of matrices over division rings
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2002
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0343