In recent years, functional codes have received much attention. In his PhD thesis, F.A.B. Edoukou investigated various functional codes linked to quadrics and Hermitian varieties defined in finite projective spaces (Edoukou, PhD Thesis, 2007). This work was continued in (Edoukou et al., Des Codes Cryptogr 56:219-233, 2010; Edoukou et al., J Pure Appl Algebr 214:1729-1739, 2010; Hallez and Storme, Finite Fields Appl 16:27-35, 2010), where the results of the thesis were improved and extended. In particular, Hallez and Storme investigated the functional codes C2H, with H a non-singular Hermitian variety in PG(N, q^2). The codewords of this code are defined by evaluating the points of H in the quadratic polynomials defined over F2. We now present the similar results for the functional code CHermQ. The codewords of this code are defined by evaluating the points of a non-singular quadric Q in PG(N, q^2) in the polynomials defining the Hermitian varieties of PG(N, q^2).
On the functional codes defined by quadrics and Hermitian varieties
BARTOLI, DANIELE;
2014
Abstract
In recent years, functional codes have received much attention. In his PhD thesis, F.A.B. Edoukou investigated various functional codes linked to quadrics and Hermitian varieties defined in finite projective spaces (Edoukou, PhD Thesis, 2007). This work was continued in (Edoukou et al., Des Codes Cryptogr 56:219-233, 2010; Edoukou et al., J Pure Appl Algebr 214:1729-1739, 2010; Hallez and Storme, Finite Fields Appl 16:27-35, 2010), where the results of the thesis were improved and extended. In particular, Hallez and Storme investigated the functional codes C2H, with H a non-singular Hermitian variety in PG(N, q^2). The codewords of this code are defined by evaluating the points of H in the quadratic polynomials defined over F2. We now present the similar results for the functional code CHermQ. The codewords of this code are defined by evaluating the points of a non-singular quadric Q in PG(N, q^2) in the polynomials defining the Hermitian varieties of PG(N, q^2).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
