Starters and related codes
The authors investigate skew starters and prove the existence of a skew starter in \(Z_v\) for all \(v\) such that \(\text{gcd}(v,6)= 1\), \(v\) is not divisible by 5 or \(v\) is divisible by 25. Next, they use skew starters to show the existence of an optimal \((6v,4,1)\) optical orthogonal code in \(Z_{6v}\) for all \(v\) such that \(\text{gcd}(v,6)= 1\). (A \((v,k,\rho)\) optical orthogonal code is a family of \((0,1)\)-sequences of length \(v\) and weight \(k\) satisfying both the auto-correlation property and the cross-correlation property.) Finally, the condition \(n\geq 8\) is proved to be necessary and sufficient for the existence of a constant weight code \((n,w,d)\) in \((Z_7)^n\) of length \(n\), minimum distance \(d= 3\), and constant Hamming weight \(w= 3\). (Frame starters are also used to prove this result).
scientific article; zbMATH DE number 1471121
scientific article