#### Vol. 11, No. 5, 2018

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On generalized MacDonald codes

### Padmapani Seneviratne and Lauren Melcher

Vol. 11 (2018), No. 5, 885–892
##### Abstract

We show that the generalized $q$-ary MacDonald codes ${C}_{n,u,t}\left(q\right)$ with parameters $\left[t\left[\genfrac{}{}{0}{}{n}{1}\right]-\left[\genfrac{}{}{0}{}{u}{1}\right],n,t{q}^{n-1}-{q}^{u-1}\right]$ are two-weight codes with nonzero weights ${w}_{1}=t{q}^{n-1}$, ${w}_{2}=t{q}^{n-1}-{q}^{u-1}$ and determine the complete weight enumerator of these codes. This leads to a family of strongly regular graphs with parameters $〈{q}^{n},{q}^{n}-{q}^{n-u},{q}^{n}-2{q}^{n-u},{q}^{n}-{q}^{n-u}〉$. Further, we show that the codes ${C}_{n,u,t}\left(q\right)$ satisfy the Griesmer bound and are self-orthogonal for $q=2$.

##### Keywords
two-weight codes, strongly regular graphs, generalized MacDonald codes, Griesmer bound
##### Mathematical Subject Classification 2010
Primary: 05C90, 94B05