On Normal q-Ary Codes in Rosenbloom-Tsfasman Metric

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...

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.

The Covering Problem in Rosenbloom-Tsfasman Spaces

We investigate the covering problem in RT spaces induced by the RosenbloomTsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen an...

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

On new completely regular q-ary codes

In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...