Mehmet Özen

Linear Codes over

AbstractWe investigate the structure of codes over

\mathbb{F}_{q}[u]/(u^s)

\mathbb{F}_q[u]/(u^s)

with Respect to the Rosenbloom---Tsfasman Metric

rings with respect to the Rosenbloom-Tsfasman (RT) metric. We define a standard form generator matrix and show how we can determine the minimum distance of a code by taking advantage of its standard form. We define MDR (maximum distance rank) codes with respect to this metric and give the weights of the codewords of an MDR code. We explore the structure of cyclic codes over

The complete weight enumerator for codes over Mn×s(R)☆

\mathbb{F}_q[u]/(u^s)

The MacWilliams identity for m-spotty weight enumerators of linear codes over finite fields

and show that all cyclic codes over

Codes over Galois rings with respect to the Rosenbloom-Tsfasman metric

\mathbb{F}_q[u]/(u^s)

Cyclic and some constacyclic codes over the ring Z 4 u { u 2 - 1 }

rings are MDR. We propose a decoding algorithm for linear codes over these rings with respect to the RT metric.

Cyclic codes over some finite quaternion integer rings

A MacWilliams identity for complete weight enumerators of codes over Mn×s(Fq) endowed with a non-Hamming metric is proved in [1]. We extend the notions introduced in [1] and prove a MacWilliams identity with respect to this new metric for the complete weight enumerator of linear codes over Mn×s(R) where R is a commutative finite ring.

Quantum codes from cyclic codes over F3 + μF3 + υF3 + μυ F3

Some of the error control codes are applied to high speed memory systems using RAM chips with either 1-bit I/O data (b=1) or 4-bit I/O data (b=4). However, modern large-capacity memory systems use RAM chips with 8, 16, or 32 bits of I/O data. A new class of codes called m-spotty byte error codes provides a good source for correcting/detecting errors in those memory systems that use high-density RAM chips with wide I/O data (e.g. 8, 16, or 32 bits). The MacWilliams identity provides the relation of weight distribution of a code and that of its dual code. The main purpose of this paper is to present a version of the MacWilliams identity for m-spotty weight enumerators of linear codes over arbitrary finite fields.

Skew Quasi Cyclic Codes over

Abstract We investigate the structure of codes over Galois rings with respect to the Rosenbloom–Tsfasman (shortly RT) metric. We define a standard form generator matrix and show how we can determine the minimum distance of a code by taking advantage of its standard form. We compute the RT-weights of a linear code given with a generator matrix in standard form. We define maximum distance rank (shortly MDR) codes with respect to this metric and give the weights of the codewords of an MDR code. Finally, we give a decoding technique for codes over Galois rings with respect to the RT metric.