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 Cn,u,t(q) with parameters [t[n 1 ] [u 1 ],n,tqn1 qu1] are two-weight codes with nonzero weights w1 = tqn1 , w2 = tqn1 qu1 and determine the complete weight enumerator of these codes. This leads to a family of strongly regular graphs with parameters qn ,qn qnu ,qn 2qnu ,qn qnu. Further, we show that the codes Cn,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