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Small Weight Codewords of Projective Geometric Codes

Tijdschriftbijdrage - Tijdschriftartikel

We investigate small weight codewords of the p-ary linear code Cj,k(n, q) generated by the incidence matrix of k-spaces and j-spaces of PG(n, q) and its dual, with q a prime power and 0 ≤ j<k<n. Firstly, we prove that all codewords of Cj,k(n, q) up to weight (3 − O ( 1/q )) times the number of j-spaces in PG(k,q) are linear combinations of at most two k-spaces (i.e. two rows of the incidence matrix). As for the dual code Cj,k(n, q)⊥, we manage to reduce both problems of determining its minimum weight (1) and characterising its minimum weight codewords (2) to the case C0,1(n, q)⊥. This implies the solution to both problem (1) and (2) if q is prime and the solution to problem (1) if q is even.
Tijdschrift: J. Comb. Theory Ser. A
Volume: 180
Jaar van publicatie:2021
BOF-keylabel:ja
IOF-keylabel:ja
BOF-publication weight:1
Auteurs:Regional
Authors from:Higher Education
Toegankelijkheid:Open