Results 21 to 30 of about 145 (141)
Constant 2-Labellings And An Application To (R, A, B)-Covering Codes
Discussiones Mathematicae Graph Theory, 2017 We introduce the concept of constant 2-labelling of a vertex-weighted graph and show how it can be used to obtain perfect weighted coverings. Roughly speaking, a constant 2-labelling of a vertex-weighted graph is a black and white colouring of its vertex
Gravier Sylvain, Vandomme Èlise
doaj +1 more source
Intelligent Information Management, 2012 We investigate how the code automorphism group can be used to study such combinatorial object as codes. Consider GF(qn) as a vector over GF(q). For any k = 0, 1, 2, 3, ???, n. Which GF(qn) exactly one subspace C of dimension k and which is invariant under the automorphism.
openaire +1 more source
Some designs and codes from L_2(q) [PDF]
Transactions on Combinatorics, 2014 For $q \in \{7,8,9,11,13,16\}$, we consider the primitive actions of $L_2(q)$ and use Key-Moori Method 1 as described in [Codes, designs and graphs from the Janko groups {$J_1$} and {$J_2$}, {\em J. Combin. Math. Combin.
Jamshid Moori +1 more
doaj
Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley +1 more source
The Complete SC-Invariant Affine Automorphisms of Polar Codes
2022 IEEE International Symposium on Information Theory (ISIT), 2022 Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders in parallel and hence has lower latency compared to that of successive cancellation list (SCL) decoding. However, some automorphisms are SC-invariant, thus are redundant in AE decoding.
Ye, Zicheng +6 more
openaire +2 more sources
Fusion systems related to polynomial representations of SL2(q)$\operatorname{SL}_2(q)$
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let q$q$ be a power of a fixed prime p$p$. We classify up to isomorphism all simple saturated fusion systems on a certain class of p$p$‐groups constructed from the polynomial representations of SL2(q)$\operatorname{SL}_2(q)$, which includes the Sylow p$p$‐subgroups of GL3(q)$\mathrm{GL}_3(q)$ and Sp4(q)$\mathrm{Sp}_4(q)$ as special cases.
Valentina Grazian +3 more
wiley +1 more source
Fault-Tolerant Logical Clifford Gates from Code Automorphisms
PRX QuantumWe study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error-correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group, and impose ...
Hasan Sayginel +4 more
doaj +1 more source
Quantum codes from algebraic curves with automorphisms
Condensed Matter Physics, 2008 Let Χ be an algebraic curve of genus g ≥ 2 defined over a field Fq of characteristic p > 0. From Χ, under certain conditions, we can construct an algebraic geometry code C.
T.Shaska
doaj +1 more source
The automorphism group of a coded system [PDF]
Transactions of the American Mathematical Society, 1996 We give a general construction of coded systems with an automorphism group isomorphic to Z ⊕ G \mathbf {Z}\oplus G where G G is any preassigned group which has a “continuous block presentation” (the isomorphism will map the shift to ( 1 ,
Fiebig, Doris, Fiebig, Ulf-Rainer
openaire +1 more source
The L$L$‐polynomials of van der Geer–van der Vlugt curves in characteristic 2
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract The van der Geer–van der Vlugt curves form a class of Artin–Schreier coverings of the projective line over finite fields. We provide an explicit formula for their L$L$‐polynomials in characteristic 2, expressed in terms of characters of maximal abelian subgroups of the associated Heisenberg groups.
Tetsushi Ito +2 more
wiley +1 more source