2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143444An 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.3 pages corrected typos: in inequality (2) changed a minus sign to plus v3.corrected 2 typos in Lemma 3.5 and added Journal-refInformation TheoryDiscrete MathematicsE.4text