A note on the code of projective plane of order four
Partha Pratim Dey, Md. Asifuzzaman · Journal of Discrete Mathematical Sciences and Cryptography · 2008
In this study we discuss a decomposition of p-ary codes C(p, 4) that are obtained from a projective plane of order 4. We are able to show that characteristic vector w ∞ of “line at infinity” belongs to the direct sum Ĉ(p, 4) ⊕ U(p, 4) if and only if p = 2 or p = 5 . Thus for p ≤ 5 , C(p, 4) = Ĉ(p, 4) ⊕ U(p, 4) , otherwise . We use the later decomposition to show that for p > 5 , , whereas we use the former decomposition to produce generator matrices of C(p, 4) for p = 2 or 5.