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• W3131474798 abstract "A Bose-Chaudhuri-Hocquenghem (BCH) is called quasi-reversible if there are consecutive elements a <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> ,⋯,a <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> in the defining set, where a <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> is a negative integer and a <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> is a positive integer. A matrix in band form presented in this article involves the use of the Newton identities and symmetric polynomial identities. This matrix is the coefficient matrix of a linear system. The solution to such a linear system is the coefficients of an error-locator polynomial for quasi-reversible BCH codes. Its computational complexity is significantly lower than BCH decoding using the linear system with coefficient matrix in column echelon form. This article also proposes a new partial syndrome matrix with radical locators and a lot of zeros. Such a matrix is still in band form. The expansion of its matrix determinant is exactly a radical-locator polynomial. Compared to the former radical-locator polynomials in the literature, the newly discovered radical-locator polynomial not only requires less storage memory but also results in computational benefits. Surprisingly, the resulting polynomials are much sparser than those for the narrow-sense BCH codes. Finally, a complete algebraic decoding algorithm for quasi-reversible BCH codes is provided. The error-locator and radical-locator polynomials of degree less than or equal to 5 are listed." @default.
• W3131474798 created "2021-03-01" @default.
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• W3131474798 date "2021-05-01" @default.
• W3131474798 modified "2023-10-16" @default.
• W3131474798 title "Algebraic Decoding of Quasi-Reversible BCH Codes Using Band Matrices" @default.
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• W3131474798 doi "https://doi.org/10.1109/tcomm.2021.3059006" @default.
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