We discuss a specific type of error-control coding using Golay codes. First we introduce the basics of coding. Then we discuss the Golay code in binary form, extended binary form, and ternary form.

A new Gray map which is both an isometry and a weight preserving map from R = F2 + vF2 + v 2F2 to F 3 2 is defined. A construction for quantum error correcting codes from cyclic codes over finite ring R = F2 + vF2 + v 2F2, v 3 = v is given.The parameters of quantum codes which are obtained from cyclic codes over R are determined.

Tables are presented of good ternary and quaternary codes and they are used in the construction of dense sphere packings. Results include 1) tables of the best ternary and quaternary constacyclic codes (including cyclic codes) up to block length 50, 2 ) a class of optimal [ n , 21 codes over GF(q), 3) the ( U + U + w I2u + U I U ) construction, a new ternary code construction technique that can...

Maximum-distance separable (MDS) convolutional codes form an optimal family of convolutional codes, the study of which is of great importance. There are very few general algebraic constructions of MDS convolutional codes. In this paper, we construct a large family of unit-memory MDS convolutional codes over Fq with flexible parameters. Compared with previous works, the field size q required to ...

In this paper a class of linear error-correcting block codes is investigated. These quasicyclic codes are closely related in structure to cyclic codes although they are not nearly as well understood. I t is shown that an important subclass of the class of cyclic codes is almost equivMent to quasicyclic codes. Also, a short computer generated list of the best quasicyclic codes of rate 1⁄2 is giv...

Several different families of quaternary codes related to Reed-Muller binary linear codes can be found in the literature. Two definitions of such families are denoted as ZRM−(r,m) and {RMs(r,m)}. In the current paper ZRM−(r,m− 1) and {RMs(r,m)} codes are shown to be equal exactly for s = 0 (0 ≤ s ≤ bm−1 2 c). Therefore, for the above-mentioned value of s, Z4-linear Reed-Muller codes with the sa...

In a recent paper, No, Golomb, Gong, Lee, and Gaal conjectured that certain binary sequences having a simple trace description possess the ideal autocorrelation property. In the present correspondence it is shown that each such sequence is balanced and, moreover, that the dual of the linear cyclic code generated by the sequence and its cyclic shifts, is a triple-error correcting code having the...

C is an (n,M, d)q code over Fq of length n with M codewords and minimum distance d. The code C can be either linear or nonlinear. A t − (v, k, λ) design D is a set X of v points together with a collection of k−subsets of X (called block) such that every t−subset of X is contained in exactly λ blocks. In this paper a new binary code ( n−1 2 , 3n−1 2 , 2.3 n−2), n ≥ 3 is developed. Some propertie...

In this paper we will study a class of concatenated coded communications systems which are built from convolutional codes and interleavers. These systems include as special cases both the classical tubo codes [1][2] and the serial concatentation of convolutional codes [4]. Our main results are a method for computing a conjectured interleaving gain exponent and for optimizing the effective free ...

Let K = Fq be a finite field. We introduce a family of projective Reed-Mullertype codes called projective Segre codes. Then we study their basic parameters and show that they are direct products of projective Reed-Muller-type codes. It turns out that the direct product of two projective Reed-Muller-type codes is again a projective Reed-Muller-type code. As a consequence we recover some results ...