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
Codes with girth 8 Tanner graph representation
Designs, Codes and Cryptography
Parity bit replenishment for JPEG 2000-based video streaming
Journal on Image and Video Processing - Special issue on distributed video coding
Performance of algebraic graphs based stream-ciphers using large finite fields
Annales UMCS, Informatica - Cryptography and data protection
On the key expansion of D(n, K)-based cryptographical algorithm
Annales UMCS, Informatica - Cryptography and data protection
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Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m≥2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2qm vertices, which has girth at least 2┌m/2┐+4. We regard these graphs as Tanner graphs of binary codes LU(m,q). We can determine the dimension and minimum weight of LU(2,q), and show that the weight of its minimum stopping set is at least q+2 for q odd and exactly q+2 for q even. We know that D(2,q) has girth 6 and diameter 4, whereas D(3,q) has girth 8 and diameter 6. We prove that for an odd prime p, LU(3,p) is a [p3,k] code with k≥(p3-2p2+3p-2)/2. We show that the minimum weight and the weight of the minimum stopping set of LU(3,q) are at least 2q and they are exactly 2q for many LU(3,q) codes. We find some interesting LDPC codes by our partial row construction. We also give simulation results for some of our codes.