Computer Science – Information Theory
Scientific paper
2011-02-13
Computer Science
Information Theory
Submitted to IEEE Transactions on Information Theory. The material in this paper was presented in part in the 2011 IEEE Intern
Scientific paper
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 transversal design. These designs can be used to derive a new family of linear codes in the Hamming space, and in particular, LDPC codes. The structure of these designs is used to obtain upper bounds on the sizes of constant dimension codes which contain the lifted MRD code. Codes which attain these bounds are constructed.
Etzion Tuvi
Silberstein Natalia
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