Results 131 to 140 of about 173,309,485 (168)
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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Automorphisms of Hyperelliptic GAG-Codes
Electronic Notes in Discrete Mathematics, 2006 Generalized algebraic-geometry codes are linear codes which generalize the well-known geometric Goppa codes, since their construction makes use of places which are not necessarily of degree one. In this paper authors determine the \(n\)-automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic ...
PICONE, Alberto, SPERA, Antonino Giorgio
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Monomial Codes With Predefined Automorphisms
2022 IEEE/CIC International Conference on Communications in China (ICCC Workshops), 2022exaly +3 more sources
Self-Orthogonal Codes From Symmetric Designs With Fixed-Point-Free Automorphisms
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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Generalized Automorphisms of Channel Codes: Properties, Code Design, and a Decoder [PDF]
, 2023 Low-density parity-check codes together with belief propagation (BP) decoding are known to be well-performing for large block lengths. However, for short block lengths there is still a considerable gap between the performance of the BP decoder and the ...
Jonathan Mandelbaum
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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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Constructing Covering Codes with Given Automorphisms
Designs, Codes and Cryptography, 1999The 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 +1 more
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On the automorphisms of generalized algebraic geometry codes
Designs, Codes and Cryptography, 2022Let \(F/GF(q)\) 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 Öke
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On the automorphism Group of a putative code
IEEE Transactions on Information Theory, 2006A 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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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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