projective codes
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Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 168
Author(s):  
Dean Crnković ◽  
Andrea Švob ◽  
Vladimir D. Tonchev

A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers ( s ≥ 2 ) of all nonzero elements in G F ( p m ) , where p ≥ 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over G F ( 4 ) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs.



Author(s):  
Najm A.M. Al-Seraji ◽  
Hossam H. Jawad

In this research, the main purposes are making partitions of the projective line, PG (1, q3), q=17, and embedding the projective line, PG (1, q ) into PG (1, q3), as well as finding some partitions of PG (2, q2) as subplanes, orbits, triangles and arcs, and studying the properties of these subsets. Furthermore, the arcs with different degrees and sizes are found besides the embedding of the projective plane, PG (2,q) into PG (2, q2). In the coding theory, there are 14 projective codes that are introduced.



2018 ◽  
Vol 54 ◽  
pp. 15-29 ◽  
Author(s):  
Mariusz Kwiatkowski ◽  
Mark Pankov ◽  
Antonio Pasini
Keyword(s):  




2014 ◽  
Vol 11 (2) ◽  
pp. 242-248
Author(s):  
Baghdad Science Journal

A (k,n)-arc is a set of k points of PG(2,q) for some n, but not n + 1 of them, are collinear. A (k,n)-arc is complete if it is not contained in a (k + 1,n)-arc. In this paper we construct complete (kn,n)-arcs in PG(2,5), n = 2,3,4,5, by geometric method, with the related blocking sets and projective codes.



2013 ◽  
Vol 7 (2) ◽  
pp. 127-145 ◽  
Author(s):  
Christine Bachoc ◽  
◽  
Alberto Passuello ◽  
Frank Vallentin ◽  


2006 ◽  
Vol 154 (12) ◽  
pp. 1693-1708 ◽  
Author(s):  
Iliya Bouyukliev
Keyword(s):  


2005 ◽  
Vol 19 (1) ◽  
pp. 145-148
Author(s):  
Sylvia Encheva


2000 ◽  
Vol 13 (4) ◽  
pp. 109-113
Author(s):  
S. Encheva ◽  
G.D. Cohen


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