The present invention concerns a device (10) for the encoding of information symbols to transmit or to record, and for the correction of errors among the symbols received or read, according to codes defined over a Galois field F.sub.q, where q is an integer greater than 2 and equal to a power of a prime number, and in which a set of elements of F.sub.q are considered which are denoted y.sub.l(j), where j=1, . . . , R with 1.ltoreq.R.ltoreq.q-1 and l=0, . . . , p-1 with p>1. Said device (10) comprises a Reed-Solomon encoder (210), a Reed-Solomon decoder (220) and a unit (500) serving to calculate the inverse of a Vandermonde matrix as well as: registers "A" (420, 430, 440, 450) in which are stored, for the encoding, said information symbols, and, for the error correction, the symbols received or read after they have been corrected, registers "S" (280, 285, 290, 295) in which are stored, for the encoding, the symbols output from said Reed-Solomon encoder (210), and, for the error correction, the symbols entering said Reed-Solomon decoder (220), and registers "Y" (410, 411, 412, 413) in which said quantities y.sub.l(j) are stored.