The Discrete Fourier Transform Over the Binary Finite Field

被引：1

作者：

Fedorenko, Sergei Valentinovich ^{[1
]}

机构：

[1] HSE Univ, Natl Res Univ, Lab Internet Things & Cyber Phys Syst, Higher Sch Econ, HSE Campus St Petersburg, St Petersburg 194100, Russia

来源：

IEEE ACCESS | 2023年 / 11卷

关键词：

Binary codes; decoding; discrete Fourier transforms; fast Fourier transforms; Galois fields; REED-SOLOMON; COMPLEXITY; COMPUTATION; ALGORITHMS; CODES;

D O I：

10.1109/ACCESS.2023.3288069

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The novel methods for binary discrete Fourier transform (DFT) computation over the finite field have been proposed. The methods are based on a binary trace calculation over the finite field and use the cyclotomic DFT. The direct DFT computational complexity has been reduced due to using the binary trace function over the finite field and the functions of trace which are stored in small tables. The computational complexity of the inverse DFT has been reduced due to representation of elements in the finite field with respect to the normal basis. The proposed methods can be used for encoding/decoding subfield subcodes, especially for binary Bose-Chaudhuri-Hocquenghem (BCH) codes. The computational complexity of the direct/inverse DFT computation methods is the smallest of all known methods.

引用

页码：62771 / 62779

页数：9

共 50 条

[1] A Method for Computation of the Discrete Fourier Transform over a Finite Field
Fedorenko, S.
PROBLEMS OF INFORMATION TRANSMISSION, 2006, 42 (02) : 139 - 151
[2] The discrete Fourier transform over a finite field with reduced multiplicative complexity
Fedorenko, Sergei V.
2011 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT), 2011, : 1200 - 1204
[3] Discrete and finite fractional Fourier transform
Wolf, KB
Group Theory and Numerical Analysis, 2005, 39 : 267 - 276
[4] A Method for Fast Computation of the Fourier Transform over a Finite Field
Trifonov, P. V.
Fedorenko, S. V.
PROBLEMS OF INFORMATION TRANSMISSION, 2003, 39 (03) : 231 - 238
[5] A Method for Fast Computation of the Fourier Transform over a Finite Field
P. V. Trifonov
S. V. Fedorenko
Problems of Information Transmission, 2003, 39 : 231 - 238
[6] Binary Discrete Fourier Transform and Its Inversion
Levinson, Howard W.
Markel, Vadim A.
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2021, 69 : 3484 - 3499
[7] BINARY WINDOWS FOR DISCRETE FOURIER-TRANSFORM
MARSHALL, FC
TEMES, GC
PROCEEDINGS OF THE IEEE, 1975, 63 (09) : 1370 - 1371
[8] DISCRETE FOURIER-TRANSFORM OVER FINITE RINGS WITH APPLICATION TO FAST CONVOLUTION
DUBOIS, E
VENETSANOPOULOS, AN
IEEE TRANSACTIONS ON COMPUTERS, 1978, 27 (07) : 586 - 593
[9] Duhamel/Hollmann-Like Discrete Fourier Transform Algorithm With the Smallest Multiplicative Complexity Over a Finite Field
Fedorenko, Sergei Valentinovich
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2020, 68 : 4813 - 4823
[10] The Design Approach for Fast Computation of Fourier Transform over a Finite Field
Deshmukh, Tejaswini P.
Dewalkar, Vrushali P.
2014 INTERNATIONAL CONFERENCE ON GREEN COMPUTING COMMUNICATION AND ELECTRICAL ENGINEERING (ICGCCEE), 2014,

← 1 2 3 4 5 →