Paper Info
Title
Self-dual codes with an automorphism of order 7 and s-extremal codes of length 68.
Abstract
This paper studies and classifies optimal binary self-dual codes having an automorphism of order 7 with 9 cycles. This classification is done by applying a method for constructing binary self-dual codes with an automorphism of odd prime order p. There are exactly 69781 inequivalent binary self-dual [64,32,12] codes with an automorphism of type 7−(9,1). As for binary [66,33,12] self-dual codes with an automorphism of type 7−(9,3) there are 1652432 such codes. We also construct more than 4 million new optimal codes of length 68 among which are the first known examples of the very elusive s-extremal self-dual codes. We prove the nonexistence of [70,35,14] codes with an automorphism of type 7−(9,7). Most of the constructed codes for all lengths have weight enumerators for which the existence was not known before.
Year
DOI
Venue
2018
10.1016/j.ffa.2017.12.001
Finite Fields and Their Applications
Keywords
Field
DocType
11T71,94B05
Prime (order theory),Combinatorics,Automorphism,Mathematics,Binary number
Journal
Volume
ISSN
Citations 
51
1071-5797
0
PageRank 
References 
Authors
0.34
16
3
Name
Order
Citations
PageRank
Nikolay Yankov1567.51
Milena Ivanova201.01
Moonho Lee342.15