Robert Rolland

On low weight codewords of generalized affine and projective Reed---Muller codes

We propose new results on low weight codewords of affine and projective generalized Reed–Muller (GRM) codes. In the affine case we prove that if the cardinality of the ground field is large compared to the degree of the code, the low weight codewords are products of affine functions. Then, without this assumption on the cardinality of the field, we study codewords associated to an irreducible but not absolutely irreducible polynomial, and prove that they cannot be second, third or fourth weight depending on the hypothesis. In the projective case the second distance of GRM codes is estimated, namely a lower bound and an upper bound on this weight are given.

The second weight of generalized Reed-Muller codes in most cases

The second weight of the Generalized Reed-Muller code of length qn and order d over the finite field with q elements is now known for d < q and d > (n − 1)(q − 1). In this paper, we determine the second weight for the other values of d which are not multiples of q − 1 plus 1. For the special case d = a(q − 1) + 1 we give an estimate.

On the existence of dimension zero divisors in algebraic function fields defined over F_q.

Let

The number of MDS [7, 3] codes on finite fields of characteristic 2

\mathbf{F}/\mathbb{F}_q

A note on Yao's theorem about pseudo-random generators

be an algebraic function field of genus

Optimization of Tree Modes for Parallel Hash Functions: A Case Study

g

A Digital Signature Scheme Based on Two Hard Problems

defined over a finite field

A Cryptographic Keys Transfer Protocol for Secure Communicating Systems

\mathbb{F}_q

Arithmetic in finite fields based on the Chudnovsky-Chudnovsky multiplication algorithm

. We obtain new results on the existence, the number and the density of dimension zero divisors of degree

Hamming distances from a function to all codewords of a Generalized Reed-Muller code of order one

g-k