The weight distribution of the self-dual $[128,64]$ polarity design code

Masaaki  Harada; Ethan  Novak; Vladimir D.  Tonchev

doi:10.3934/amc.2016032

Article Contents

2016, Volume 10, Issue 3: 643-648. Doi: 10.3934/amc.2016032

This issue Previous Article On self-dual MRD codes Next Article Constructions and bounds for mixed-dimension subspace codes

The weight distribution of the self-dual $[128,64]$ polarity design code

1.
Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579
2.
Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931

Received: July 2015

Revised: February 2016

Published: August 2016

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Abstract

The weight distribution of the binary self-dual $[128,64]$ code being the extended code $C^{*}$ of the code $C$ spanned by the incidence vectors of the blocks of the polarity design in $PG(6,2)$ [11] is computed. It is shown also that $R(3,7)$ and $C^{*}$ have no self-dual $[128,64,d]$ neighbor with $d \in \{ 20, 24 \}$.

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Mathematics Subject Classification: Primary: 94B30; Secondary: 05B25.

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