We investigate the generalized bilinear forms graph Γd over a residue class ring Zps . We show that Γd is a connected vertex transitive graph, and completely determine its independence number, clique number, chromatic number and maximum cliques. We also prove that cores of both Γd and its complement are maximum cliques. The graph Γd is useful for error-correcting codes. We show that every large...

We present a maximum-separable-distance (MDS) code suitable for computing erasure resilient codes for large word lengths. Given n data blocks (words) of any even bit length w the Circulant Cauchy Codes compute m ≤ w+1 code blocks of bit length w using XOR-operations, such that every combination of n data words and code words can reconstruct all data words. The number of XOR bit operations is at...

Myelodysplastic syndromes (MDSs) are a clonal bone marrow (BM) disease characterized by ineffective hematopoiesis, dysplastic maturation and progression to acute myeloid leukemia (AML). Methylation silencing of HRK has been found in several human malignancies. In this study, we explored the association of HRK methylation status with its expression, clinical parameters and MDS subtypes in MDS pa...

The hull of a linear code is the intersection itself with its dual respect to certain inner product. Both Euclidean and Hermitian hulls are theorical practical significance. In this paper, we construct several new classes maximum distance separable (MDS) codes via (extended) generalized Reed-Solomon (GRS) determine their or hulls. As consequence, four MDS flexible dimensions six constructed. ap...

We construct quantum MDS codes with parameters $$ [\![ q^2+1,q^2+3-2d,d ]\!] _q$$ for all $$d \leqslant q+1$$ , \ne q$$ . These are shown to exist by proving that there classical generalised Reed–Solomon which contain their Hermitian dual. constructions include many were previously known but in some cases these new. go on prove if $$d\geqslant q+2$$ then is no $$[n,n-d+1,d]_{q^2}$$ code contain...

We investigate the possibility of using error correcting codes in digital signatures. A scheme combining one way functions and a MDS code is presented and analyzed. We then study an attack upon this scheme and upon more general ones called "random knapsack schemes" involving a linear combination Xi T(xi,i) of the message elements x i .

In this paper a new construction of MDS array codes is introduced. In order to obtain a code with this property, the parity-check matrix is constructed just using a superregular matrix by blocks composed by powers of the companion matrix of a primitive polynomial. Also a decoding algorithm for these codes is introduced.

FEC (Forward Error Correction) techniques are widely used in streaming data applications. The increasing popularity of streaming over wireless links, however, poses additional challenges because of its high data loss characteristic and the energy/computation limitation of wireless terminals. Consequently, traditional FEC schemes might no longer be suitable. And new FEC scheme is desirable in th...

In the Distributed Storage Systems (DSSs), encoded fraction of information is stored in the distributed fashion on different chunk servers. Recently a new paradigm of Fractional Repetition (FR) codes have been introduced, in which, encoded data information is stored on distributed servers, where encoding is done using a Maximum Distance Separable (MDS) code and a repetition code. In this work, ...