The dimensions of LU(3,q) codes

Details The dimensions of LU(3,q) codes The dimensions of LU(3,q) codes

2008-01-31

arxiv.org/abs/0802.0015v8

Journal of Combinatorial Theory, Series A 116 (2009) 1073-1079

Mathematics

Combinatorics

The missing elements in the base $/beta$ are added. Typo in the proof of Lemma 10 is corrected

Scientific paper

A family of LDPC codes, called LU(3,q) codes, has been constructed from q-regular bipartite graphs. Recently, P. Sin and Q. Xiang determined the dimensions of these codes in the case that q is a power of an odd prime. They also obtained a lower bound for the dimension of an LU(3,q) code when q is a power of 2. In this paper we prove that this lower bound is the exact dimension of the LU(3,q) code. The proof involves the geometry of symplectic generalized quadrangles, the representation theory of Sp(4,q), and the ring of polynomials.

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