We consider primitive Reed-Solomon (RS) codes over the field F 2m  of length n=2 m -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 23  and F 24 , 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 23 , F 24  , and F 25 .
['Fabian Lim', 'Marc P. C. Fossorier', 'Aleksandar Kavcic']
Code Automorphisms and Permutation Decoding of Certain Reed–Solomon Binary Images