Generators and weights of polynomial codes
Cazaran, J and Kelarev, A (1997) Generators and weights of polynomial codes. Archiv Math. (Basel, Germany), 69 . pp. 479486. Official URL: http://link.springer.de/link/service/journals/00013/ AbstractSeveral authors have established that many classical codes are ideals in certain ring constructions. Berman, in the case of characteristic two, and Charpin, in the general case, proved that all generalized ReedMuller codes coincide with powers of the radical of the quotient ring
$A=F_q[x_1,\ldots,x_n]/(x_1^{q_1}1,\ldots,x_n^{q_n}1),$
where $F_q$ is a finite field, $p=\char F_q>0$ and $q_i=p^{c_i}$, for $i=1,\ldots,n$,
and gave formulas for their Hamming weights. These codes form an important class containing many codes of practical value. Errorcorrecting codes in similar ring constructions $A$ have also been considered by Poli. Our paper contains new results that generalise and strengthen several facts obtained earlier by other authors. Item Type:  Article 

Keywords:  errorcorrecting codes 

ID Code:  185 

Deposited By:  utas eprints 

Deposited On:  16 Jun 2005 

Last Modified:  18 Jul 2008 19:39 

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