We obtain a technique to reduce the computational complexity associated with decoding of Hermitian codes. In particular, we propose a method to compute the error locations and values using an uni-variate error locator and an uni-variate error evaluator polynomial. To achieve this, we introduce the notion of Semi-Erasure Decoding of Hermitian codes and prove that decoding of Hermitian codes can ...

We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret and disguise it by considering its shortened expanded code the base field. Considering provides safeguard against distinguisher attacks based on Schur product. Moreover, without using cyclic or quasi-cyclic structure obtain key size reduction of near...

In this work, we study the performance of Reed–Solomon codes against adversarial insertion-deletion (insdel) errors. We prove that over fields size $n^{O(k)}$ there are notation="LaTeX">$[n,k]$ Reed-Solomon can decode from notation="L...

So far, we have examined three types of codes: • Atomic Codes: Hamming, Hadamard, Reed-Solomon, and Reed-Muller codes • Random Codes • Concatenated Codes: Forney and Justesen Codes The last two types of codes are asymptotically good. However, while the Random Codes are nonconstructible, the Concatenated Codes provide us with an explicit way of producing asymptotically good codes. Further in the...

A low-complexity systematic encoding algorithm for polar codes with Reed-Solomon kernel is presented. The proposed method relies on fast Fourier transform based ReedSolomon encoding techniques. Application of polar codes in storage systems is considered.

In this paper we compute the second generalized Hamming weight of the evaluation codes associated to complete bipartite graphs. The main result depends on the minimum distance and second generalized Hamming weight of the generalized Reed-Solomon codes.

In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes. And we give some results on Hermitian self-dual codes, which are the extended cyclic duadic codes.