scholarly journals Constructing Gray maps from combinatorial geometries

2014 ◽  
Vol 63 (2) ◽  
pp. 147-161
Author(s):  
PAŞA Abdullah; YILDIZ
Keyword(s):  
Gray Maps ◽  
Combinatorial Geometries

A class of constacyclic codes over the ring Z4[u,v]/ and their Gray images

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2237-2248 ◽  
Author(s):  
Habibul Islam ◽  
Om Prakash
Keyword(s):  
Cyclic Codes ◽  
Constacyclic Codes ◽  
Gray Maps ◽  
Permutation Equivalent ◽  
Quasi Cyclic Codes

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.

Independence in Combinatorial Geometries of Rank Three

1975 ◽  
Vol 18 (2) ◽  
pp. 217-221
Author(s):  
Japheth Hall
Keyword(s):  
Combinatorial Geometry ◽  
Combinatorial Geometries

The class of all combinatorial geometries of rank three shall coincide with the class of all pairs (V, S) such that V is a set and S is a collection of non-empty subsets of V such that each pair of distinct elements of V belong to exactly one member of S. (See [3].)Consider a combinatorial geometry (V, S) of rank three.

Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries

1988 ◽  
Vol 4 (1) ◽  
pp. 323-332 ◽  
Author(s):  
Joseph P. S. Kung ◽  
James G. Oxley
Keyword(s):  
Combinatorial Geometries

A desarguesian theorem for algebraic combinatorial geometries

COMBINATORICA ◽  
1985 ◽  
Vol 5 (3) ◽  
pp. 237-239 ◽  
Author(s):  
B. Lindström
Keyword(s):  
Combinatorial Geometries

Double Circulant Self-Dual and LCD Codes Over ℤp2

2019 ◽  
Vol 30 (03) ◽  
pp. 407-416
Author(s):  
Daitao Huang ◽  
Minjia Shi ◽  
Patrick Solé
Keyword(s):  
Lower Bounds ◽  
Minimum Distance ◽  
Exact Enumeration ◽  
Lcd Codes ◽  
Gray Maps ◽  
Double Circulant Codes ◽  
Circulant Codes

We study double circulant LCD codes over [Formula: see text] for all odd primes [Formula: see text] and self-dual double circulant codes over [Formula: see text] for primes [Formula: see text]. We derive exact enumeration formulae, and asymptotic lower bounds on the minimum distance of the [Formula: see text]-ary images of these codes by the classical Gray maps.

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