Symbol-pair code is a new coding framework which is proposed to correct errors in the symbolpair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pairdistance five or six. ...

We prove that the fast pseudo-Hadamard transform (FPHT) over a finite field has a bounded branch number. We shall demonstrate that the transform has an efficient implementation for various platforms compared to an equal dimension MDS code. We prove that when using a CS-Cipher[3] like construction the weight of any 2R trail is bounded for the case of an 8 × 8 transform. We show that the FPHT can...

AbslracrMDS codes possess several properties that make them an ideal choice for type41 hybrid-ARQ protocols. These properties indude “strong separability”, “strong invertibility”, and excellent reliability performance when used for simultaneous error detection and correction. In this paper these properties are shown to lead to a natural definition of an MDS type-I1 hybrid-ARQ protocol. An (n, k...

Given an LCD group code C in a group algebra KG, we inspect kinship between C and G, more precisely between the subgroup structures of G and C. When C is MDS, the inter relation between K and G becomes more impressive. Application of Sylow theorem facilitated us to explore the inter relation between G and K (when C is LCD and MDS) in more general way and finally we get the result of Cruz and Wi...

Both MDS and Euclidean self-dual codes have theoretical and practical importance and the study of MDS self-dual codes has attracted lots of attention in recent years. In particular, determining existence of q-ary MDS self-dual codes for various lengths has been investigated extensively. The problem is completely solved for the case where q is even. The current paper focuses on the case where q ...

A typical communication system consists of a channel code to transmit signals reliably over a noisy channel. In general the channel code is a set of codewords which are used to carry information over the channel. This thesis deals with Elias upper bound on the normalized rate for Euclidean space codes and on codes which are close to the generalized Singleton bound, like MaximumDistance Separabl...

This semi-tutorial paper discusses the connections between the dimension/length profile (DLP) of a linear code, which is essentially the same as its " generalized Hamming weight hierarchy " 111, and the complexity of its minimal trellis diagram. These connections are close andtdeep. DLP duality is closely related to trellis duality. The DLP of a code gives tight bounds on its state and branch c...

MDS (e.g. Reed-Solomon) codes have many desirable properties which make them the code of choice in network scenarios and distributed coding schemes. An average binary weight enumerator of Reed-Solomon (RS) codes is derived assuming a binomial distribution of the bits in a non-zero symbol. Lower bounds on the average binary minimum distance of the ensemble of binary images of a Reed-Solomon code...

In this correspondence, we present a new description of the X-Code, a class of MDS array code, using skews. The X-Codes result in codewords that are arrays of size n × n, where n is prime. Our new description does not require n to be prime but requires n to be an odd number with smallest prime factor greater than 3. We prove that our description results in a distance-3 MDS code and also show wh...

MDS codes are erasure-correcting codes that can correct the maximum number of erasures for a given number of redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting all the remaining data in the code, the original information can be recovered. However, it was shown that in order to recover a single symbol erasure, only a fraction of 1/...