MinT - Information on Result #1417563

Information on Result #1417563

Linear OOA(3²²⁹, 5440, F₃, 2, 40) (dual of [(5440, 2), 10651, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3²²⁹, 5440, F₃, 40) (dual of [5440, 5211, 41]-code), using

discarding factors / shortening the dual code based on linear OA(3²²⁹, 6582, F₃, 40) (dual of [6582, 6353, 41]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(3²⁰, 21, F₃, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,3)), using
    - dual of repetition code with length 21 [i]
  2. linear OA(3²⁰⁹, 6561, F₃, 40) (dual of [6561, 6352, 41]-code), using
    - an extension C_e(39) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,39], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²²⁹, 2720, F₃, 3, 40) (dual of [(2720, 3), 7931, 41]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²²⁹, 2720, F₃, 4, 40) (dual of [(2720, 4), 10651, 41]-NRT-code)	[i]		OOA Folding