Results 131 to 140 of about 374 (164)

On the automorphisms of generalized algebraic geometry codes [PDF]

Designs, Codes, and Cryptography, 2022
Let \(F/GF(q)\) denote an algebraic function field over the finite field \(GF(q)\) with \(q\) elements, where \(q\) is a power of a prime number. For each place \(P\) of \(F\) of degree \(n\) there is a \(GF(q)\)-isomomorphism of vector spaces, \(\phi_P:F_P\to GF(q^n)\cong GF(q)^n\).
Engin Senel, Figen Oke
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On the Weights of Linear Codes With Prescribed Automorphisms [PDF]

IEEE Transactions on Information Theory, 2023
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Gaojun Luo, Xiwang Cao, Martianus Frederic Ezerman, San Ling   +3 more
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Monomial Codes With Predefined Automorphisms

2022 IEEE/CIC International Conference on Communications in China (ICCC Workshops), 2022
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On Binary Self-Dual Codes With Automorphisms

IEEE Transactions on Information Theory, 2008
In this correspondence, we present some results concerning a decomposition of binary self-dual codes possessing an automorphism of certain type. Two applications are given. The first one is the classification of all extremal doubly even self-dual codes of length having an automorphism of order .
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On Calculation of Monomial Automorphisms of Linear Cyclic Codes [PDF]

Lobachevskii Journal of Mathematics, 2018
© 2018, Pleiades Publishing, Ltd. A description of the monomial automorphisms group of an arbitrary linear cyclic code in term of polynomials is presented.
Aida Gainutdinova
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Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms [PDF]

Discrete Mathematics, 2003
In this paper, we consider a method for constructing non-binary self-orthogonal codes from symmetric designs with fixed-point-free automorphisms. All codes over GF(3) and GF(7) derived from symmetric 2-(v,k,λ) designs with fixed-point-free automorphisms ...
Masaaki Harada, Vladimir D Tonchev
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Automorphism Groups of Convolutional Codes

SIAM Journal on Applied Mathematics, 1978
Let 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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Constructing Covering Codes with Given Automorphisms

Designs, Codes and Cryptography, 1999
The authors consider the problem of finding upper bounds on \(K(n,r)\), the minimum number of words in a binary code of length \(n\) and covering radius \(r\). Constructions of covering codes give these bounds on \(K(n,r)\). It is shown how computer searches for covering codes can be speed up by requiring that the code has a given (not necessarily full)
Patric R. J. Östergård, William D. Weakley   +1 more
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On the automorphism Group of a putative code

IEEE Transactions on Information Theory, 2006
A long standing open question in coding theory is whether a binary self-dual [72,36,16] code exists. It was shown recently that the automorphism group order of such code is equal to 2imiddot3 jmiddot5middot7, 2imiddot3jmiddot7, 2imiddot3jmiddot5, or 2imiddot3 j for some nonnegative integers i and j.
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