On generalized MacDonald codes

Seneviratne, Padmapani; Melcher, Lauren

doi:10.2140/involve.2018.11.885

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On generalized MacDonald codes

Padmapani Seneviratne and Lauren Melcher

Vol. 11 (2018), No. 5, 885–892

DOI: 10.2140/involve.2018.11.885

Abstract

We show that the generalized $q$ -ary MacDonald codes $C_{n, u, t} (q)$ with parameters $[t [\binom{n}{1}] - [\binom{u}{1}], n, t q^{n - 1} - q^{u - 1}]$ 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 $C_{n, u, t} (q)$ 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

Milestones

Received: 23 August 2017

Revised: 8 December 2017

Accepted: 14 December 2017

Published: 2 April 2018

Communicated by Joshua Cooper

Authors

Padmapani Seneviratne
Department of Mathematics Texas A&M University–Commerce Commerce, TX United States

Lauren Melcher
Department of Mathematics Texas A&M University–Commerce Commerce, TX United States

Vol. 11, No. 5, 2018