CHARACTERIZATIONS FOR SEVERAL CLASSES OF ALTERNATIVE CODES

Several classes of optimal ternary cyclic codes

Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight new classes of optimal ternary cyclic codes with parameters [3−1, 3−1−2m, 4], according to a result on the non-existence of solutions to a certain equation o...

Soft De oding of Several Classes of Array Codes

Several Classes of (2m - 1, w, 2) Optical Orthogonal Codes

Optical orthogonal codes have applications in optical code-division multiple access communication systems and other wide band code-division multiple environments. They can also be used to construct protocol sequences for multiuser collision channel without feedback, and constant weight codes for error detection and correction. In this paper, we construct four classes of (2 − 1; w; 2) cyclotomic...

Several Classes of Concatenated Quantum Codes: Constructions and Bounds

In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of Ashikhmin–Litsyn–Tsfasman and Matsumoto. We also give a polynomial-time decoding algorithm for the codes that can decode up to one fourth of the lower bound on the minimum distance o...

Several Classes of $p$-ary Linear Codes with Few Weights

Few weights codes have been an important topic of coding theory for decades. In this paper, a class of two-weight and three-weight codes for the homogeneous metric over the chain ring R = Fp + uFp + · · ·+ uFp are constructed. These codes are defined as trace codes. They are shown to be abelian. Their homogeneous weight distributions are computed by using exponential sums. In particular, we giv...