The Covering Problem in Rosenbloom-Tsfasman Spaces

Distance Graphs of Metric Spaces with Rosenbloom - Tsfasman metric

Rosenbloom and Tsfasman introduced a new metric (RT metric) which is a generalization of the Hamming metric. In this paper we study the distance graphs of spaces Zn q and Sn with Rosenbloom -Tsfasman metric. We also describe the degrees of vertices, components and the chromatic number of these graphs. Distance graphs of general direct product spaces also described.

Macwilliams Duality and the Rosenbloom–tsfasman Metric

A new non-Hamming metric on linear spaces over finite fields has recently been introduced by Rosenbloom and Tsfasman [8]. We consider orbits of linear groups preserving the metric and show that weight enumerators suitably associated with such orbits satisfy MacWilliams-type identities for mutually dual codes. Furthermore, we show that the corresponding weight spectra of dual codes are related b...

MacWilliams Extension Theorems and the Local-Global Property for Codes over Rings

The MacWilliams extension theorem is investigated for various weight functions over finite Frobenius rings. The problem is reformulated in terms of a local-global property for subgroups of the general linear group. Among other things, it is shown that the extension theorem holds true for poset weights if and only if the underlying poset is hierarchical. Specifically, the Rosenbloom-Tsfasman wei...

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

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...