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On the dimensions of certain LDPC codes based on q-regular bipartite graphs

Peter Sin·Qing Xiang
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Abstract

An explicit construction of a family of binary LDPC codes called LU(3,q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a 4-dimensional symplectic vector space and the action of the symplectic group and its subgroups.

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Peter Sin, Qing Xiang. 2007-12-04. On the dimensions of certain LDPC codes based on q-regular bipartite graphs. https://arxiv.org/abs/cs/0506011

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