L codes and number systems

Hybrid Regenerating Codes for Distributed Storage Systems

Distributed storage systems are mainly justified due to their ability to store data reliably over some unreliable nodes such that the system can have long term durability. Recently, regenerating codes are proposed to make a balance between the repair bandwidth and the storage capacity per node. This is achieved through using the notion of network coding approach. In this paper, a new variation ...

Codes from Algebraic Number Fields

INTRODUCTION The geometry of numbers, coding theory, the Riemann hypothesis the list of key words for this lecture can be read äs a partial history of the Stichting Mathematisch Centrum. The lecture itself attempts to reflect the spirit of the SMC by displaying a new connection between these subjects. Using ideas from the geometry of numbers one can construct a class of codes from algebraic num...

Codes and Systems

Path covering number and L(2,1)-labeling number of graphs

A path covering of a graph G is a set of vertex disjoint paths of G containing all the vertices of G. The path covering number of G, denoted by P (G), is the minimum number of paths in a path covering of G. An k-L(2, 1)-labeling of a graph G is a mapping f from V (G) to the set {0, 1, . . . , k} such that |f(u) − f(v)| ≥ 2 if dG(u, v) = 1 and |f(u) − f(v)| ≥ 1 if dG(u, v) = 2. The L(2, 1)-label...

Maximal Order Codes over Number Fields

— We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the ...