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arXiv · 1102.2593

Codes and Designs Related to Lifted MRD Codes

Tuvi Etzion·Natalia Silberstein
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Abstract

Lifted maximum rank distance (MRD) codes, which are constant dimension codes, are considered. It is shown that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. A slightly different representation of this design makes it similar to a $q-$analog of a transversal design. The structure of these designs is used to obtain upper bounds on the sizes of constant dimension codes which contain a lifted MRD code. Codes which attain these bounds are constructed. These codes are the largest known codes for the given parameters. These transversal designs can be also used to derive a new family of linear codes in the Hamming space. Bounds on the minimum distance and the dimension of such codes are given.

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Tuvi Etzion, Natalia Silberstein. 2011-02-13. Codes and Designs Related to Lifted MRD Codes. https://doi.org/10.1109/isit.2011.6033969

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