Abstract
The notion of normality of codes in Hamming metric is extended to the codes in Rosenbloom-Tsfasman metric (RT-metric, in short). Using concepts of partition number and l-cell of codes in RT-metric, we establish results on covering radius and normality of q-ary codes in this metric. We also examine the acceptability of various coordinate positions of q-ary codes in this metric. And thus, by exploring the feasibility of applying amalgamated direct sum method for construction of codes, we analyze the significance of normality in RT-metric.
Highlights
Covering properties of codes have unique significance in coding theory, and covering radius, one of the four fundamental parameters, of a code is important in several respects [1]
In order to improve upon the bounds on covering radius, various construction techniques that use two or more known codes to construct a new code were proposed over the last few decades
To improve upon the bounds related to covering radius of codes obtained using this method, the notion of normality which facilitates a construction technique known as amalgamated direct sum (ADS) was introduced for binary linear codes by Graham and Sloane in [5]
Summary
Covering properties of codes have unique significance in coding theory, and covering radius, one of the four fundamental parameters, of a code is important in several respects [1]. Considering the fact that it is a geometric property of codes that characterizes maximal error correcting capability in the case of minimum distance decoding, covering radius had been extensively studied by many researchers (see, e.g., [2, 3] and the literature therein) especially with respect to the conventional Hamming metric. It has evolved into a subject in its own right mainly because of its practical applicability in areas such as data compression, testing, and write-once memories and because of the mathematical beauty that it possesses.
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