An association between primitive and non-primitive BCH codes using monoid rings

Quasi-Primitive Rings and Density Theory

On primitive BCH codes with unequal error protection capabilities

where H i m ) = -mlog2 ( U ) (1 crjlog, (1 a). In this correspondence we present new estimates of the relative error term improving the known results. Our approach is based on investigating upper bounds for absolute values of Krawtchouk polynomials. Actually, this is just a refinement of an idea due to P. Sol6 [ 161. The bounds obtained are quite tight. Particularly, for t fixed our estimate is...

The Minimum Distance of Some Narrow-Sense Primitive BCH Codes

Due to wide applications of BCH codes, the determination of their minimum distance is of great interest. However, this is a very challenging problem for which few theoretical results have been reported in the last four decades. Even for the narrow-sense primitive BCH codes, which form the most well-studied subclass of BCH codes, there are very few theoretical results on the minimum distance. In...

An Exactification of the Monoid of Primitive Recursive Functions

We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.

Alternant and BCH codes over certain rings

Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of xs − 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use of the modified Berlekamp-Massey algorithm to correct errors and erasures is presented. Furthermore...