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• W2148145328 abstract "We consider primitive Reed-Solomon (RS) codes over the field F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2m</sub> of length n=2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</sup> -1. Building on Lacan 's results for the case of binary extension fields, we show that the binary images of certain two-parity symbol RS [n, n-2, 3] code, have a code automorphism subgroup related to the general linear group GL(m, 2). For these codes, we obtain a code automorphism subgroup of order m! GL(m,2). An explicit algorithm is given to compute a code automorphism (if it exists), that sends a particular choice of m binary positions, into binary positions that correspond to a single symbol of the RS code. If one such automorphism exists for a particular choice of m binary symbol positions, we show that there are at least m! of them. Computationally efficient permutation decoders are designed for the two-parity symbol RS [n, n-2, 3] codes. Simulation results are shown for the additive white Gaussian noise (AWGN) channel. For the finite fields F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>23</sub> and F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>24</sub> , we go on to derive subgroups of code automorphisms, belonging to binary images of certain RS codes that have three-parity symbols. A table of code automorphism subgroup orders, computed using the Groups, Algorithms, and Programming (GAP) software, is tabulated for the fields F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>23</sub> , F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>24</sub> , and F <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>25</sub> ." @default.
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• W2148145328 date "2010-10-01" @default.
• W2148145328 modified "2023-09-30" @default.
• W2148145328 title "Code Automorphisms and Permutation Decoding of Certain Reed–Solomon Binary Images" @default.
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• W2148145328 doi "https://doi.org/10.1109/tit.2010.2059633" @default.
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