On Self-dual and LCD Double Circulant Codes over a Non-chain Ring*

2019 ◽  
Vol 28 (5) ◽  
pp. 1018-1024
Author(s):  
Ting Yao ◽  
Shixin Zhu ◽  
Xiaoshan Kai
Keyword(s):  
Chain Ring ◽  
Double Circulant Codes ◽  
Circulant Codes

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.

Double circulant constructions of the Leech lattice

2000 ◽  
Vol 69 (3) ◽  
pp. 287-297 ◽  
Author(s):  
Robin Chapman
Keyword(s):  
Leech Lattice ◽  
Double Circulant Codes ◽  
Circulant Codes

AbstractWe consider the problem of finding, for each even number m, a basis of orthogonal vectors of length in the Leech lattice. We give such a construction by means of double circulant codes whenever m = 2p and p is a prime not equal to 11. From this one can derive a construction for all even m not of the form 2· 11r.

EISENSTEIN LATTICES, GALOIS RINGS AND QUATERNARY CODES

2006 ◽  
Vol 02 (02) ◽  
pp. 289-303 ◽  
Author(s):  
PHILIPPE GABORIT ◽  
ANN MARIE NATIVIDAD ◽  
PATRICK SOLÉ
Keyword(s):  
Modular Lattice ◽  
Orthogonal Basis ◽  
Galois Ring ◽  
Galois Rings ◽  
Type Ii ◽  
Dual Codes ◽  
Type Ii Codes ◽  
Quaternary Codes ◽  
Double Circulant Codes ◽  
Circulant Codes

Self-dual codes over the Galois ring GR(4,2) are investigated. Of special interest are quadratic double circulant codes. Euclidean self-dual (Type II) codes yield self-dual (Type II) ℤ4-codes by projection on a trace orthogonal basis. Hermitian self-dual codes also give self-dual ℤ4-codes by the cubic construction, as well as Eisenstein lattices by Construction A. Applying a suitable Gray map to self-dual codes over the ring gives formally self-dual 𝔽4-codes, most notably in length 12 and 24. Extremal unimodular lattices in dimension 38, 42 and the first extremal 3-modular lattice in dimension 44 are constructed.

scholarly journals Double circulant codes from two class association schemes

2007 ◽  
Vol 1 (1) ◽  
pp. 45-64 ◽  
Author(s):  
Steven T. Dougherty ◽  
◽  
Jon-Lark Kim ◽  
Patrick Solé ◽  
◽  
...  
Keyword(s):  
Association Schemes ◽  
Double Circulant Codes ◽  
Circulant Codes
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