Polynomial Codes Over Certain Finite Fields

a._) into the 2-tuple (P(0), P(a), P(a:), P(1 ); this m-tuple might be some encoded message and the corresponding 2n-tuple is to be transmitted. This mapping of m symbols into 2 symbols will be shown to be (2 m)/2 or (2 m 1)/2 symbol correcting, depending on whether m is even or odd. A natural correspondence is established between the field elements of K and certain binary sequences of length n. Under this correspondence, code E may be regarded as a mapping of binary sequences of mn bits into binary sequences of n2 bits. Thus code E can be interpreted to be a systematic multiple-error-correcting code of binary sequences.