Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles
Designs, Codes and Cryptography
Note: The dimensions of LU(3,q) codes
Journal of Combinatorial Theory Series A
Recent Developments in Low-Density Parity-Check Codes
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
Some low-density parity-check codes derived from finite geometries
Designs, Codes and Cryptography
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An explicit construction of a family of binary low-density parity check (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 four-dimensional (4-D) symplectic vector space and the action of the symplectic group and its subgroups