On Isometric Error-Correcting Codes over Finite Fields of Prime Order

Structure of finite wavelet frames over prime fields

‎This article presents a systematic study for structure of finite wavelet frames‎ ‎over prime fields‎. ‎Let $p$ be a positive prime integer and $mathbb{W}_p$‎ ‎be the finite wavelet group over the prime field $mathbb{Z}_p$‎. ‎We study theoretical frame aspects of finite wavelet systems generated by‎ ‎subgroups of the finite wavelet group $mathbb{W}_p$.

Geometric Codes over Fields of Odd Prime Power Order

We obtain improved bounds for the minimum weight of the dual codes associated with the codes from finite geometries in the case of odd order, and some results that apply also to the dual codes of non-desarguesian planes of odd order.

Finite-connectivity systems as error-correcting codes.

We investigate the performance of parity check codes using the mapping onto Ising spin systems proposed by Sourlas [Nature (London) 339, 693 (1989); Europhys. Lett. 25, 159 (1994)]. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C checks per message bit. We show, using the replica method, that these codes saturate Shan...

Cross-Error Correcting Integer Codes over ℤ2m

Classification of the Deletion Correcting Capabilities of Reed-Solomon Codes of Dimension 2 Over Prime Fields

Deletion correction codes have been used for transmission synchronization and, more recently, tracing pirated media. A generalized Reed-Solomon (GRS) code, denoted by GRSk(l,q,alpha,v), is a code of length l over GF(q) with qk codewords. These codes have an efficient decoding algorithm and have been widely used for error correction and detection. It was recently demonstrated that GRS codes are ...