Quantum error-correcting codes play an important role in both quantum communication and quantum computation. It has experienced a great progress since the establishment of the connections between quantum codes and classical codes (see [4]). It was shown that the construction of quantum codes can be reduced to that of classical linear error-correcting codes with certain self-orthogonality proper...

Error-correcting pairs were introduced in 1988 in the pre-print [24] that appeared in [26], and were found independently in [18], as a general algebraic method of decoding linear codes. These pairs exist for several classes of codes. However little or no study has been made for characterizing those codes. This article is an attempt to fill the vacuum left by the literature concerning this subje...

Symbol-pair codes are proposed to protect against pair-errors in symbol-pair read channels. The research of with the largest possible minimum distance is great significance since such have best error-correcting capability. A code meeting Singleton bound called a maximum separable (MDS) code. In this paper, two new classes MDS by utilizing repeated-root cyclic over finite fields odd characterist...

In this paper, we describe a procedure for constructing q– ary [N, 3, N−2]–MDS codes, of length N ≤ q+1 (for q odd) or N ≤ q+2 (for q even), using a set of non–degenerate Hermitian forms in PG(2, q).

We will construct an MDS(= the most distance separable) code C which admits a decomposition C = ⊕iCi such that every factor is still MDS. An effective way of decoding will be also discussed.

A multidimensional file is one whose data are characterized by several attributes, each specified in a given domain. A partial match query on a multidimensional file extracts all data whose attributes match the values of one or more attributes specified in the query. The disk allocation problem of a multidimensional file F on a database system with multiple disks accessible in parallel is the p...

A set of n + k points (k > 0) in projective space of dimension n is said to be an (n + k)-arc if there is no hyperplane containing any n + 1 points of the set. It is well-known that for the projective space PG(n, q), this is equivalent to a maximum distance separable linear code with symbols in the finite field GF(q), of length n + k, dimension n + 1, and distance d = k that satisfies the Singl...

Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process. Recently, array XOR codes have attracted attention for storage systems due to their burst error recovery performance and easy arithmetic based on Exclusive OR (XOR)-only logic operations. Array BP-XOR...

Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This application of LCD codes renewed the interest in the construction of LCD codes having a large minimum distance. MDS codes are optimal in the sense that the m...

It is known that maximum distance separable and maximum distance profile convolutional codes exist over large enough finite fields of any characteristic for all parameters (n, k, δ). It has been conjectured that the same is true for convolutional codes that are strongly maximum distance separable. Using methods from linear systems theory, we resolve this conjecture by showing that, over a large...