On s-sum-sets (s odd) and three-weight projective codes

2006 ◽  
pp. 68-76 ◽  
Author(s):  
Mercè Griera
Keyword(s):  
Projective Codes

scholarly journals Codes and Projective Multisets

10.37236/1375 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Stefan Dodunekov ◽  
Juriaan Simonis
Keyword(s):  
Coding Theory ◽  
Linear Codes ◽  
Full Length ◽  
Self Duality ◽  
Projective Codes ◽  
Matrix Free

The paper gives a matrix-free presentation of the correspondence between full-length linear codes and projective multisets. It generalizes the Brouwer-Van Eupen construction that transforms projective codes into two-weight codes. Short proofs of known theorems are obtained. A new notion of self-duality in coding theory is explored.

The graphs of projective codes

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

scholarly journals Bounds for projective codes from semidefinite programming

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

scholarly journals Cyclotomic Trace Codes

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 168
Author(s):  
Dean Crnković ◽  
Andrea Švob ◽  
Vladimir D. Tonchev
Keyword(s):  
Quantum Codes ◽  
Strongly Regular Graphs ◽  
Block Designs ◽  
Regular Graphs ◽  
Combinatorial Structures ◽  
Trace Codes ◽  
Strongly Regular ◽  
Projective Codes

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.

scholarly journals Partitions on the Projective Line and Plane of Order 17k,k=1,2,3

2019 ◽  
Vol 54 (6) ◽  
Author(s):  
Najm A.M. Al-Seraji ◽  
Hossam H. Jawad
Keyword(s):  
Projective Plane ◽  
Coding Theory ◽  
Projective Line ◽  
Projective Codes

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.

scholarly journals On the binary projective codes with dimension 6

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

scholarly journals Projective codes which satisfy the chain condition

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

scholarly journals The construction of Complete (kn,n)-arcs in The Projective Plane PG(2,5) by Geometric Method, with the Related Blocking Sets and Projective Codes

2014 ◽  
Vol 11 (2) ◽  
pp. 242-248
Author(s):  
Baghdad Science Journal
Keyword(s):  
Projective Plane ◽  
Geometric Method ◽  
Blocking Sets ◽  
Projective Codes

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.

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