Higher weight spectra of codes from Veronese threefolds

Codes from Veronese and Segre Embeddings and Hamada's Formula

This article grew out of our attempt to understand the methods of [6] in the context of Veronese and Segre embeddings of projective spaces over finite fields. Let q= p, p a prime, and P denote the n dimensional projective space over the finite field Fq . The zero set in P of a homogeneous polynomial of degree l over Fq is called a l hypersurface in P. Let k be a field of characteristic p. Let C...

The weight hierarchies and generalized weight spectra of the projective codes from degenerate quadrics

The weight hierarchies and generalized weight spectra of the projective codes from degenerate quadrics in projective spaces over finite fields are determined. These codes satisfy also the chain conditions.

Two-weight and three-weight codes from trace codes over

We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the non-chain ring Fp+uFp+ vFp+uvFp, where u 2 = 0, v = 0, uv = vu. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. With a linear Gray map, we obtain a class of abelian three-weight codes and two-weight codes...

Higher weight distribution of linearized Reed-Solomon codes

Let m, d and k be positive integers such that k ≤ me , where e = (m, d). Let p be an prime number and π a primitive element of Fpm . To each ~a = (a0, · · · , ak−1) ∈ F k pm , we associate the linearized polynomial f~a(x) = k−1 ∑ j=0 ajx p , as well as the sequence c~a = (f~a(1), f~a(π), · · · , f~a(π pm−2)). Let C = {c~a | ~a ∈ F k pm} be the cyclic code formed by the sequences c~a’s. We call ...

Codes from Higher - Dimensional Varieties