Patent ID: 8347190

Claim:
A method of encoding data for transmission from a source to a destination over a communication channel by means of an error-correcting code, said error-correcting code being defined by a parity check matrix (H) having or comprising a Vandermonde structure, the method comprising the steps of: receiving a plurality of data symbols (I l ); and preparing at least one codeword (c) of said error-correcting code at an encoding station, said codeword to be transmitted over said communication channel and comprising said plurality of data symbols (I l ) and a plurality of parity symbols (P j ); wherein said step of preparing said codeword (c) comprises the steps of: selecting one out of a plurality of parity patterns ({i j } j=0, . . . , 2t-1) , said parity pattern ({i j } j=0, . . . , 2t-1 ) determining the positions at which said parity symbols (P j ) are located within said codeword (c); and determining said parity symbols (P j ) on the basis of said data symbols (I l ) and said selected parity pattern ({i j } j=10, . . . , 2t-1 ); characterized in that determining at least one of said parity symbols (P j ) is based on a step of evaluating a polynomial (Λ (j) , Λ) of a degree that is no larger than the number of parity symbols (P j ) in said codeword (c); wherein said polynomial (Λ (j) ) is a Lagrange polynomial, i.e., Λ ( j ) ⁡ ( a i k ) = { 1 y i j ⁢ fork = j , 0 fork ≠ j , wherein {a 0 , a 1 , . . . , a n-1 } is a set of n distinct and non-zero elements of a finite field, the positive integer n denoting the length of said codeword (c), {y 0 , y 1 , . . . , y n-1 } is a set of n non-zero elements of said finite field, j is a positive integer denoting the parity symbol, and i k is a positive integer denoting the position of the k-th parity symbol in said codeword according to said selected parity pattern.