Patent ID: 7398456

Claim:
A method of encoding over a Galois field F q , where q is an integer greater than 2 and equal to a power of a prime number, in which a word v′=(v′ 0 ,v′ 1 , . . . , v′ n′−1 ) is calculated, where n′≧3, belonging to an MDS linear cyclic code C′ of dimension (n′−m), where 1≦m≦n′−2, on the basis of a word a=(a 0 , a 1 , . . . , a n−m−1 ) of information symbols, where m<n<n′, in which a set s=(s 0 ,s 1 , . . . , s n−1 ) of strictly increasing integers, with s 0 ≧0 and s n−1 ≦n′−1, having been predetermined, the method comprising the steps of: a) forming the polynomial a ⁡ ( x ) ≡ ∑ i = m n - 1 ⁢ a i - m ⁢ x s i , b) calculating the remainder r(x) of the Euclidean division of a(x) by the polynomial g ⁡ ( x ) ≡ ∑ p = 0 m ⁢ g p ⁢ x p generating said code C′, c) calculating the polynomial v * ⁡ ( x ) = a ⁡ ( x ) - r ⁡ ( x ) ≡ ∑ i = 0 n ′ - 1 ⁢ v i * ⁢ x i , corresponding to the word v*=(v* 0 , v* 1 , . . . , v* n′−1 ), and d) taking v′=v* if s m−1 =m−1; otherwise obtaining said word v′ by taking: v _ ′ = v * + ∑ j = 0 s m - m - 1 ⁢ f j ⁢ Γ _ j ( 1 ) in which the words Γ j of length n′ are defined by: Γ j i =g i−j for j≦i≦j+m, and Γ j i =0 otherwise, and in which the elements f j of F q are calculated by means of the equations (1) in which, for the (s m −m) values of i<s m not belonging to the set s, each component v′ i ; is taken equal to a respective predetermined constant.