MinT - Information on Result #1408339

Information on Result #1408339

Linear OOA(3⁸⁶, 1610, F₃, 2, 17) (dual of [(1610, 2), 3134, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3⁸⁶, 1610, F₃, 17) (dual of [1610, 1524, 18]-code), using

discarding factors / shortening the dual code based on linear OA(3⁸⁶, 2196, F₃, 17) (dual of [2196, 2110, 18]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(3⁸, 9, F₃, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using
    - dual of repetition code with length 9 [i]
  2. linear OA(3⁷⁸, 2187, F₃, 17) (dual of [2187, 2109, 18]-code), using
    - an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(3⁸⁶, 805, F₃, 3, 17) (dual of [(805, 3), 2329, 18]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3⁸⁶, 805, F₃, 4, 17) (dual of [(805, 4), 3134, 18]-NRT-code)	[i]		OOA Folding