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pro vyhledávání: '"Matsui, Hajime"'
Autor:
Matsui, Hajime
名古屋大学博士学位論文 学位の種類 : 博士(数理学)(課程) 学位授与年月日:平成11年9月30日 松井一氏の博士論文として提出された
Externí odkaz:
http://hdl.handle.net/2237/15793
Publikováno v:
In Finite Fields and Their Applications August 2023 89
Akademický článek
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Autor:
Nakashima, Norihiro, Matsui, Hajime
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 dimension of the related projective space is equal to 1. The minimum distanc
Externí odkaz:
http://arxiv.org/abs/1412.4365
Autor:
Matsui, Hajime
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 affine variety codes. Our lemma corresponds to the non-systematic encoding
Externí odkaz:
http://arxiv.org/abs/1211.4728
Autor:
Matsui, Hajime
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 variety codes is proposed. Our procedure is achieved by multidimensional D
Externí odkaz:
http://arxiv.org/abs/1210.0083
Autor:
Matsui, Hajime
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 algebraic geometry codes. This lemma states that two vector spaces, one cor
Externí odkaz:
http://arxiv.org/abs/1208.5429
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) codes, and Hermitian codes. Although it is known that the systematic e
Externí odkaz:
http://arxiv.org/abs/0811.4033
Autor:
Matsui, Hajime, Mita, Seiichi
This paper proposes a novel algorithm for finding error-locators of algebraic-geometric codes that can eliminate the division-calculations of finite fields from the Berlekamp-Massey-Sakata algorithm. This inverse-free algorithm provides full performa
Externí odkaz:
http://arxiv.org/abs/0705.0286
Autor:
Matsui, Hajime, Mita, Seiichi
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 numerical examples. We employ the recurrence from the Gr\"obner basis of t
Externí odkaz:
http://arxiv.org/abs/cs/0703104