Symplectic spread-based generalized Kerdock codes View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2007-02

AUTHORS

S. González, C. Martínez, I. F. Rúa

ABSTRACT

Kerdock codes (Kerdock, Inform Control 20:182–187, 1972) are a well-known family of non-linear binary codes with good parameters admitting a linear presentation in terms of codes over the ring (see Nechaev, Diskret Mat 1:123–139, 1989; Hammons et al., IEEE Trans Inform Theory 40:301–319, 1994). These codes have been generalized in different directions: in Calderbank et al. (Proc Lond Math Soc 75:436–480, 1997) a symplectic construction of non-linear binary codes with the same parameters of the Kerdock codes has been given. Such codes are not necessarily equivalent. On the other hand, in Kuzmin and Nechaev (Russ Math Surv 49(5), 1994) the authors give a family of non-linear codes over the finite field F of q = 2l elements, all of them admitting a linear presentation over the Galois Ring R of cardinality q2 and characteristic 22. The aim of this article is to merge both approaches, obtaining in this way new families of non-linear codes over F that can be presented as linear codes over the Galois Ring R. The construction uses symplectic spreads. More... »

PAGES

213-226

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10623-006-9031-8

DOI

http://dx.doi.org/10.1007/s10623-006-9031-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1005381036


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