Some results on NQR codes (Q1283214)

\textit{P. D. Tiu} and \textit{D. T. Wallace} [IEEE Trans. Inf. Theory 40, 946-949 (1994; Zbl 0824.94028)] have constructed a new class of linear codes called norm quadratic residue codes \(C_p\) for \(p\) a prime of the form \(4n+1\). They have shown that \(\dim C_p\leq p\), minimum distance \(d\geq p-1\), \(C_p\) is weakly self dual and the weight of each codeword is divisible by 4. In the present paper the authors show that a similar construction works for primes of the form \(4n-1\). They collect some more results for any odd prime \(p\). In the paper it is shown that \(\dim C_p=p\), \(C_p\) is normal and its covering radius is \(\frac{p(p-1)}{2}\).