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Automorphism Groups of Convolutional Codes
SIAM Journal on Applied Mathematics, 1978Let K be the monomial group of degree n, over the field $F = GF( q )$, and let $K^\infty $ denote the group of mappings $x:\mathbb{Z} \to K:i \mapsto x^{( i )} $. For any sequence $v ( D ) = \sum {v_i D^i } $, with $v_i \in F^n $, and any x in $K^\infty $, the x-image of $v( D )$ is defined to be $v( D )x = \sum {v_i x^{( i )} D^i } $.
Delsarte, Ph., Piret, Ph.
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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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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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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)
Schulz, Ralph-Hardo +1 more
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On Calculation of Monomial Automorphisms of Linear Cyclic Codes
Lobachevskii Journal of Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kugurakov V. +2 more
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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.
GIULIETTI, Massimo, Korchmaros G.
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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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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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