Introduction. A code is a mapping from a vector space of dimension m over a finite field K (denoted by V,(K)) into a vector space of higher dimension n> m over the same field (V (K)). K is usually taken to be the field of two elements Z., in which ease it is a mapping of m-tuples of binary digits (bits) into n-tuples of binary digits. If one transmits n bits, the additionaln m bits are" redundant" and allow one to recover the original message in the event that noise corrupts the signal during trans-mission and causes some bits () f the code to be inerror. A multiple-error-correcting code of order s consists of a code which maps m-tuples of zeros and ones into n-tuples of zeros and ones, where ra and n both depend on s, and a decoding procedure whichrecovers the message completely, assuming no more than s errors occur during transmission in the vector of n bits. The Hamming code [1] is an example of a systematic one bit error-correcting code. We present here a new class of redundant codes along with a decoding procedure.

Let K be a field of degree n over the field of two elements Z. K contains 2 elements. Its multiplieative group is eyelie and is generated by powers of c where is the root of a suitable irreducible polynomial over Z.. We discuss here a code E which maps m-tuples of K into 2-tuplcs of K. Consider the polynomial P (x) of degree m 1