Zobrazeno 1 - 10
of 75
pro vyhledávání: '"Jennifer D. Key"'
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing. 34:57-66
For $$m\ge 4$$ even, the duals of p-ary codes, for any prime p, from adjacency matrices for the m-ary 2-cube $$Q^m_2$$ are shown to have subcodes with parameters $$[m^2,2m-2,m]$$ for which minimal PD-sets of size $$\frac{m}{2}$$ are constructed, henc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::73cf86719b9b86f679e80c0034bd5289
https://doi.org/10.1007/s00200-020-00481-5
https://doi.org/10.1007/s00200-020-00481-5
Publikováno v:
Journal of Applied Mathematics and Computing. 61:461-479
Codes from adjacency matrices from the Hamming graphs $$H^k(n,m)$$ are examined for the property of being special LCD codes. The special property involves being able to propose a feasible decoding algorithm for the binary codes, and also to deduce th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e325d0e9e5f3a019e01e4108d06878e7
https://doi.org/10.1007/s12190-019-01259-w
https://doi.org/10.1007/s12190-019-01259-w
Publikováno v:
Graphs and Combinatorics. 35:633-652
We examine binary and ternary codes from adjacency matrices of the Peisert graphs, $${\mathcal {P}}^*(q)$$ , and the generalized Peisert graphs, $$G{\mathcal {P}}^*(q)$$ , in particular those instances where the code is LCD and the dual of the code f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ec71ac165dcd59047da02f588a58912f
https://doi.org/10.1007/s00373-019-02019-0
https://doi.org/10.1007/s00373-019-02019-0
Publikováno v:
Graphs and Combinatorics. 34:163-192
Studies of the p-ary codes from the adjacency matrices of uniform subset graphs $$\varGamma (n,k,r)$$ and their reflexive associates have shown that a particular family of codes defined on the subsets are intimately related to the codes from these gr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8ab186b7cfe1803334f76f74d79bad0e
https://doi.org/10.1007/s00373-017-1862-8
https://doi.org/10.1007/s00373-017-1862-8
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing. 29:227-244
It is shown how LCD codes with a particularly useful feature can be found from row spans over finite fields of adjacency matrices of graphs by considering these together with the codes from the associated reflexive graphs and complementary graphs. Ap
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3dafe1129b812ea6bdf4a9a225ca1ccd
https://doi.org/10.1007/s00200-017-0339-6
https://doi.org/10.1007/s00200-017-0339-6
Publikováno v:
Discrete Mathematics. 340:722-728
It is shown that for n ź 5 and r ź n - 1 2 , if an ( n , M , 2 r + 1 ) binary code exists, then the r th-order Reed-Muller code R ( r , n ) has s -PD-sets of the minimum size s + 1 for 1 ź s ź M - 1 , and these PD-sets correspond to sets of trans
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::350049b22d9bae5a88b6e67fa77edf14
https://doi.org/10.1016/j.disc.2016.11.031
https://doi.org/10.1016/j.disc.2016.11.031
Publikováno v:
Advances in Mathematics of Communications. 11:179-185
We show explicitly that the dimension of the ternary code of the Hall plane of order 9 is greater than the dimension of the ternary code of the desarguesian plane of order 9. The proof requires finding a word with some defined properties in the dual
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7bd22d05c25e24660765d1a3b7296712
https://doi.org/10.3934/amc.2017011
https://doi.org/10.3934/amc.2017011
Autor:
Padmapani Seneviratne, Jennifer D. Key
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing. 27:399-412
We show how to find s-PD-sets of the minimal size $$s+1$$s+1 for the $$\left[ \frac{q^n-q^u}{q-1},n,q^{n-1}-q^{u-1}\right] _q $$qn-quq-1,n,qn-1-qu-1q MacDonald q-ary codes $$C_{n,u}(q)$$Cn,u(q) where $$n \ge 3$$nź3 and $$1 \le u \le n-1$$1≤u≤n-1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::09eb9105f1ccc1c7f0e193cd2f81f57d
https://doi.org/10.1007/s00200-016-0286-7
https://doi.org/10.1007/s00200-016-0286-7
Publikováno v:
Advances in Mathematics of Communications. 9:211-232
We examine the binary codes $C_2(A_i+I)$ from matrices $A_i+I$ where $A_i$ is an adjacency matrix of a uniform subset graph $\Gamma(n,3,i)$ of $3$-subsets of a set of size $n$ with adjacency defined by subsets meeting in $i$ elements of $\Omega$, whe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bfcb806b3f111683a8abd2c6b1d01fa2
https://doi.org/10.3934/amc.2015.9.211
https://doi.org/10.3934/amc.2015.9.211
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing. 25:363-382
We examine the ternary codes $$C_3(A_i+I)$$C3(Ai+I) from matrices $$A_i+I$$Ai+I where $$A_i$$Ai is an adjacency matrix of a uniform subset graph $$\Gamma (n,3,i)$$Γ(n,3,i) of $$3$$3-subsets of a set of size $$n$$n with adjacency defined by subsets m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ed3e2bb4ba4fb615c499109a01f2e15c
https://doi.org/10.1007/s00200-014-0233-4
https://doi.org/10.1007/s00200-014-0233-4