Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights are obtained from some functions with low Walsh spectrum in odd characteristic. Numerical results show that some of the linear codes obtained are optimal or al...

We show that if a linear code admits an extension, then it necessarily admits a linear extension. There are many linear codes that are known to admit no linear extensions. Our result implies that these codes are in fact maximal. We are able to characterize maximal linear (n, k, d)q-codes as complete (weighted) (n, n − d)-arcs in PG(k−1, q). At the same time our results sharply limit the possibi...

In this paper, we study cyclic stabiliser codes over Fp of length dividing p + 1 for some positive integer t. We call these t-Frobenius codes or just Frobenius codes for short. We give methods to construct them and show that they have efficient decoding algorithms. An important subclass of stabiliser codes are the linear stabiliser codes. For linear Frobenius codes we have stronger results: We ...

Linear complementary dual codes (LCD) are linear codes satisfying C ∩C = {0}. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal matrices. Some asymptotic results are derived.

A linear code is said to be proper in error detection over a symmetric memoryless channel if its undetected error probability is an increasing function of the channel symbol error probability. A proper code performs well in error detection in the sense that the better the channel, the better the performance, which makes the code appropriate for use in channels where the symbol error probability...

In an earlier paper the authors studied simplex codes of type α and β over Z4 and obtained some known binary linear and nonlinear codes as Gray images of these codes. In this correspondence, we study weight distributions of simplex codes of type α and β over Z2s . The generalized Gray map is then used to construct binary codes. The linear codes meet the Griesmer bound and a few non-linear codes...