Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles

We find lower bounds on the minimum distance and characterize codewords of small weight in low-density parity check codes defined by (dual) classical generalized quadrangles. We analyze the geometry of the non-singular parabolic quadric in PG(4, q) to find information about the low-density parity check codes defined by Q(4, q), W(q) and H(3, q2 ). For W(q) and H(3, q2 ), we are able to describe small weight codewords geometrically. For Q(4, q), q odd, and for H(4, q2 )D , we improve the best known lower bounds on the minimum distance, again only using geometric arguments. Similar results are also presented for the LDPC codes LU(3, q) given in [10]

• Type: Conference
• Year: 2007
• Where: DCC
• Authors: Jon-Lark Kim, Keith E. Mellinger, Leo Storme
• Keywords: Computer Graphics, DCC 2007, Low-density Parity Check, Lower Bounds, Parity Check Codes