Learn More
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of p-ary 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(More)
Reed-Solomon codes, a type of BCH codes, are widely employed in communication systems, storage devices and consumer electronics. This fact demonstrates the importance of BCH codes – a family of cyclic codes – in practice. In theory, BCH codes are among the best cyclic codes in terms of their error-correcting capability. A subclass of BCH codes are the(More)
The theory of cyclotomy dates back to Gauss and has a number of applications in combinatorics, coding theory, and cryptography. Cyclotomy over a residue class ring \BBZv can be divided into classical cyclotomy or generalized cyclotomy, depending on v prime or composite. In this paper, we introduce a generalized cyclotomy of order d over(More)
We present unified constructions of optical orthogonal codes (OOCs) using other combinatorial objects such as cyclic linear codes and frequency hopping sequences. Some of obtained OOCs are optimal or asymptotically optimal with respect to the Johnson bound. Also, we are able to show the existence of new optimal frequency hopping sequences (FHSs) with(More)
Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. Strictly optimal FHSs are those FHSs with optimal partial Hamming autocorrelation irrespective of the correlation window length. In this paper, strictly optimal FHSs are investigated from a(More)
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q-ary linear codes with few weights employing general quadratic forms over the finite field F q ${\mathbb {F}}_{q}$ is proposed, where q is an odd prime power. This generalizes some(More)
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. Let m = 2ℓ + 1 for an integer ℓ ≥ 1 and π be a generator of GF(3 m) *. In this paper, a class of cyclic codes C (u,v) over GF(3) with two nonzeros π u and π v is(More)
Bent functions as optimal combinatorial objects are difficult to characterize and construct. In the literature, bent idempotents are a special class of bent functions and few constructions have been presented, which are restricted by the degree of finite fields and have algebraic degree no more than 4. In this paper, several new infinite families of bent(More)
The characterization and construction of bent functions are challenging problems. The paper generalizes the constructions of Boolean bent functions by Mesnager [33], Xu et al. [40] and p-ary bent functions by Xu et al. [41] to the construction of p-ary weakly regular bent functions and presents new infinite families of p-ary weakly regular bent functions(More)