Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of pary linear codes with two or three weights are constructed from quadratic Bent functions over the finite field F p , where p is an odd prime. They include some earlier linear codes as special cases. The weight distributions of these linear codes are also determined.

Abstract-Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied. In this paper, we show that for any Ksparse signal x, if a sensing matrix A satisfies the restricted isometry property (RIP) with restricted isometry constant (RIC) δK+1 < 1/ √ K + 1, then under some constraints on the minimum magnitude of nonzero elements of x, OMP exactly recovers the support of x from its measurements y = Ax + v in K iterations, where v is a noise vector that is ℓ2 or ℓ∞ bounded. This sufficient condition is sharp in terms of δK+1 since for any given positive integer K and any 1/ √ K + 1 ≤ δ < 1, there always exists a matrix A satisfying the RIP with δK+1 = δ for which OMP fails to recover a K-sparse signal x in K iterations. Also, our constraints on the minimum magnitude of nonzero elements of x are weaker than existing ones. Moreover, we propose worst-case necessary conditions for the exact support recovery of x, characterized by the minimum magnitude of the nonzero elements of x.Index Terms-Compressed sensing (CS), restricted isometry property (RIP), restricted isometry constant (RIC), orthogonal matching pursuit (OMP), support recovery.

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a class of threeweight cyclic codes over GF(p) whose duals have two zeros is presented, where p is an odd prime. The weight distribution of this class of cyclic codes is settled. Some of the cyclic codes are optimal. The duals of a subclass of the cyclic codes are also studied and proved to be optimal.

Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of constructing two-weight and three-weight linear codes of Ding et al. [6] and Zhou et al. [27] to general weakly regular bent functions and determines the weight distributions of these linear codes. It solves the open problem of Ding et al. [6]. Further, this paper constructs new linear codes with two or three weights and presents the weight distributions of these codes. They contains some optimal codes meeting certain bound on linear codes.