The Minimum Distance of Graph Codes

We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other geometries. We give results on the minimum distances of the codes

Face Recognition Using Fractal Codes

In this paper we propose a new method for face recognition using fractal codes. Fractal codes represent local contractive, affine transformations which when iteratively applied to range-domain pairs in an arbitrary initial image result in a fixed point close to a given image. The transformation parameters such as brightness offset, contrast factor, orientation and the address of the corresponding domain for each range are used directly as features in our method. Features of an unknown face image are compared with those pre-computed for images in a database. There is no need to iterate, use fractal neighbor distances or fractal dimensions for comparison in the proposed method. This method is robust to scale change, frame size change and rotations as well as to some noise, facial expressions and blur distortion in the imag

New bounds for bb-Symbol Distances of Matrix Product Codes

Matrix product codes are generalizations of some well-known constructions of codes, such as Reed-Muller codes, $[u+v,u-v]$-construction, etc. Recently, a bound for the symbol-pair distance of a matrix product code was given in \cite{LEL}, and new families of MDS symbol-pair codes were constructed by using this bound. In this paper, we generalize this bound to the $b$-symbol distance of a matrix product code and determine all minimum $b$-symbol distances of Reed-Muller codes. We also give a bound for the minimum $b$-symbol distance of codes obtained from the $[u+v,u-v]$-construction, and use this bound to construct some $[2n,2n-2]_q$-linear $b$-symbol almost MDS codes with arbitrary length. All the minimum $b$-symbol distances of $[n,n-1]_q$-linear codes and $[n,n-2]_q$-linear codes for $1\leq b\leq n$ are determined. Some examples are presented to illustrate these results

Linear block and convolutional MDS codes to required rate, distance and type

Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required error-correcting capability and required types. Infinite series of block codes with rate approaching a given rational $R$ with $0<R<1$ and relative distance over length approaching $(1-R)$ are designed. These can be designed over fields of given characteristic $p$ or over fields of prime order and can be specified to be of a particular type such as (i) dual-containing under Euclidean inner product, (ii) dual-containing under Hermitian inner product, (iii) quantum error-correcting, (iv) linear complementary dual (LCD). Convolutional codes to required rate and distance and infinite series of convolutional codes with rate approaching a given rational $R$ and distance over length approaching $2(1-R)$ are designed. The designs are algebraic and properties, including distances, are shown algebraically. Algebraic explicit efficient decoding methods are referenced