10.1007/s10623-007-9079-0
doi
pub.1041732343
dimensions_id
Mathematical Sciences
Electrical and Computer Engineering, University of Calgary, T2N 1N4, Calgary, AB, Canada
University of Calgary
https://scigraph.springernature.com/explorer/license/
Coprimitive sets and inextendable codes
2008-06
2008-06-01
false
articles
research_article
113-124
http://link.springer.com/10.1007%2Fs10623-007-9079-0
Complete (n,r)-arcs in PG(k−1,q) and projective (n,k,n−r)q-codes that admit no projective extensions are equivalent objects. We show that projective codes of reasonable length admit only projective extensions. Thus, we are able to prove the maximality of many known linear codes. At the same time our results sharply limit the possibilities for constructing long non-linear codes. We also show that certain short linear codes are maximal. The methods here may be just as interesting as the results. They are based on the Bruen–Silverman model of linear codes (see Alderson TL (2002) PhD. Thesis, University of Western Ontario; Alderson TL (to appear) J Combin Theory Ser A; Bruen AA, Silverman R (1988) Geom Dedicata 28(1): 31–43; Silverman R (1960) Can J Math 12: 158–176) as well as the theory of Rédei blocking sets first introduced in Bruen AA, Levinger B (1973) Can J Math 25: 1060–1065.
en
2019-04-15T09:27
readcube_id
c6cb7ca6d74e03a91ee9f605cedd3d8d7dfbc44237c1bb7b21707c88d97fdfe4
Mathematical Sciences, University of New Brunswick Saint John, E2L 4L5, Saint John, NB, Canada
University of New Brunswick
47
T. L.
Alderson
A. A.
Bruen
Pure Mathematics
0925-1022
Designs, Codes and Cryptography
1573-7586
1-3
Springer Nature - SN SciGraph project