MacWilliams Type identities for $m$-spotty Rosenbloom-Tsfasman weight enumerators over finite commutative Frobenius rings

TL;DR

This paper extends MacWilliams identities to $m$-spotty Rosenbloom-Tsfasman weight enumerators for linear codes over finite commutative Frobenius rings, aiding error detection and correction in memory systems.

Contribution

It introduces MacWilliams type identities for $m$-spotty RT weight enumerators over finite commutative Frobenius rings, generalizing previous binary code results.

Findings

Derived MacWilliams identities for $m$-spotty RT weight enumerators.

Applicable to linear codes over finite commutative Frobenius rings.

Enhances error correction analysis in memory systems.

Abstract

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. \"{O}zen and V. Siap [7] proved a MacWilliams identity for the $m$-spotty Rosenbloom-Tsfasman (shortly RT) weight enumerators of binary codes. The main purpose of this paper is to present the MacWilliams type identities for $m$-spotty RT weight enumerators of linear codes over finite commutative Frobenius rings.