6 citations · 12 across the 7 of their papers we have counts for
7 papers
Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces
Norihiro Nakashima, Hajime Matsui
A projective Reed-Muller (PRM) code, obtained by modifying a (classical) Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimens…
Lemma for Linear Feedback Shift Registers and DFTs Applied to Affine Variety Codes
Hajime Matsui
In this paper, we establish a lemma in algebraic coding theory that frequently appears in the encoding and decoding of, e.g., Reed-Solomon codes, algebraic geometry codes, and affi…
Decoding a Class of Affine Variety Codes with Fast DFT
Hajime Matsui
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine vari…
Fast Erasure-and-Error Decoding and Systematic Encoding of a Class of Affine Variety Codes
Hajime Matsui
In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algeb…
Computation of Grobner basis for systematic encoding of generalized quasi-cyclic codes
Vo Tam Van, Hajime Matsui, Seiichi Mita
Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC)…
Encoding via Gröbner bases and discrete Fourier transforms for several types of algebraic codes
Hajime Matsui, Seiichi Mita
We propose a novel encoding scheme for algebraic codes such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed-Solomon codes and present nume…