Results 141 to 150 of about 374 (164)
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On automorphism groups of the Hermitian codes
IEEE Transactions on Information Theory, 1995The author studies algebraic-geometric Goppa codes that can be obtained from Hermitean curves over \(GF(q^2)\). He determines the automorphism group of these codes in the interesting cases to be isomorphic to a subgroup of automorphisms of the curve that have a special form. This group has order \(q^3 (q^2-1)\).
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On automorphism groups of certain Goppa codes
Designs, Codes and Cryptography, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Massimo Giulietti, Gábor Korchmáros
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Affine Automorphism Group of Polar Codes
IEEE Transactions on Information TheoryzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zicheng Ye +5 more
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The automorphism groups of the Delsarte-Goethals codes
Designs, Codes and Cryptography, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Automorphisms of Extremal Self-Dual Codes
IEEE Transactions on Information Theory, 2010Let C be a binary extremal self-dual code of length n ? 48. We prove that for each ? ? Aut(C) of prime order p ? 5 the number of fixed points in the permutation action on the coordinate positions is bounded by the number of p-cycles. It turns out that large primes p, i.e., n-p small, seem to occur in |Aut(C)| very rarely.
Stefka Bouyuklieva +2 more
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On the Automorphism Groups of Affine-Invariant Codes.
Designs, Codes and Cryptography, 1996Let \(A\) be a group code. An affine-invariant code is a group code which is invariant under the action of the affine group \(AGL (1, p^m)\). If \(C\) denotes a cyclic code of length \(p^m - 1\) over a finite field \(K\) the extended code \(\overline C\) is an affine-invariant code if and only if its permutation group (the permutations acting on the ...
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On the Automorphism Group of Generalized Hermitian Codes
IEEE Transactions on Information Theory, 2013We determine the full automorphism group of the Generalized Hermitian curve, denoted by GH, which generalizes the Hermitian curve. The automorphism group of a code is important in Coding Theory, and in this way, we determine completely the automorphism group of the one-point AG codes over the GH curve.
Alonso Sepúlveda Castellanos +1 more
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Codes with simple automorphism groups, II
Archiv der Mathematik, 1978For primesl≧ 11 of the form 2m+1,m an odd prime, the automorphism group of the extended (l+1, (l+1)/2) quadratic residue code overGF(q) is simple. If the automorphism group properly containsPSL 2 (l), then for all primes of the above form the stability group of a point is simple. Application is made to the casesl=7, 11 and 23.
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Automorphisms of Constant Weight Codes and of Divisible Designs
Designs, Codes and Cryptography, 2000After showing how to construct a constant weight code \(C(D)\) from a divisible design \(D\), the authors study how the automorphism groups of \(D\) and \(C(D)\) are related. The main result is the following: Aut\((D)\) induces a faithful group of automorphisms on \(C(D)\), which either is equal to Aut\((C(D))\) or has index equal to \(2\) in Aut\((C(D)
Ralph-Hardo Schulz +1 more
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Decomposing and shortening codes using automorphisms
IEEE Trans. Inf. Theory, 1986Codes possessing certain types of automorphisms are examined. In one case, the code can be decomposed as a direct sum of two subcodes, which can be viewed as shorter length codes. In a second case, the code itself corresponds to a shorter length code. Related results and applications are given.
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