AN IDENTITY BETWEEN THE m-SPOTTY ROSENBLOOM-TSFASMAN WEIGHT ENUMERATORS OVER FINITE COMMUTATIVE FROBENIUS RINGS

MacWilliams 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...

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...

MacWilliams Type Identity for M-Spotty Rosenbloom-Tsfasman Weight Enumerator of Linear Codes over Finite Ring

MacWilliams Identity for m-spotty Weight Enumerators over Finite Ring ⋆

Recently, the m-spotty byte error control codes are used in computer memory systems to detect and correct errors. These codes are essential to make the memory systems more reliable. In this paper, we introduce the m-spotty weights and m-spotty weight enumerator of linear codes over the ring Fp[u]/(u s). Moreover, we prove a MacWilliams type identity for m-spotty weight enumerator.

Finite Commutative Rings with a MacWilliams Type Relation for the m-Spotty Hamming Weight Enumerators

Let R be a finite commutative ring. We prove that a MacWilliams type relation between the m-spotty weight enumerators of a linear code over R and its dual hold, if and only if, R is a Frobenius (equivalently, Quasi-Frobenius) ring, if and only if, the number of maximal ideals and minimal ideals of R are the same, if and only if, for every linear code C over R, the dual of the dual C is C itself...