Patent ID: 7634711

Claim:
Computer implemented Method of coding information symbols according to a code defined on a Galois field F q , where q is an integer greater than 2 and equal to a power of a prime number, and of length n=p(q−1), where p is an integer greater than 1, comprising steps of: a) choosing a p-tuple of integers (t 1 , . . . , t p ) such that q− 1 >t 1 >t 2 > . . . >tp >0, and a p-tuple of diagonal square matrices (Y 1 , . . . , Y p ) of dimension (q−1) on F q such that, for any i(1≦i≦q−1), the p elements in position (i,i) of these matrices Y 1 , . . . , Y p are different in pairs, b) placing the information symbols successively in p words a 1 of length (q−1−t l ) (where l=1, . . . ,p), c) forming words u l (where l=1, . . . ,p) of length (q−1), which constitute the components of the a precoded word u =[ u, 1 u 2 . . . u p ], by supplementing the corresponding word a l by means of redundant symbols so that u l is orthogonal to a matrix H (t l ) , where the matrices H (t) are defined by H (t) ij =γ i(j-1) (1≦i≦t, 1≦j≦q−1), where γ is a symbol chosen from amongst the primitive elements of F q , and d) forming a code word v =[ v 1 v 2 . . . v p ] where each word v (l=1, . . . , p) is of length (q−1), by resolving a system of equations { v _ 1 + v _ 2 + … + v _ p = u _ l , v _ 1 ⁢ Y 1 + v _ 2 ⁢ Y 2 + … + v _ p ⁢ Y p = u _ 2 , v _ 1 ⁢ Y 1 2 + v _ 2 ⁢ Y 2 2 + … + v _ p ⁢ Y p 2 = u _ 3 , ⋯ v _ 1 ⁢ Y 1 p - 1 + v _ 2 ⁢ Y 2 p - 1 + … + v _ p ⁢ Y p p - 1 = u _ p .