Maximal arcs in projective three-spaces and double-error-correcting cyclic codes (Q5929840)

Let \(C_{1,t}^{(m)}\) denote the binary cyclic code of length \(2^m-1\) with defining zeros \(\alpha\) and \(\alpha^t\), where \(\alpha\) is a primitive element in \(\text{GF} (2^m)\). The authors give a new proof using maximal arcs in \(\text{PG} (3,2^m)\) of the following theorem:NEWLINENEWLINENEWLINELet \(m\geq 4\), \(t=2^{2h}-2^h+1\) and \(\text{gcd} (m,h)=1\). Then \(C^{(m)}_{1,t}\) has minimum distance 5.