MinT - Information on Result #1521846

Information on Result #1521846

Linear OOA(3⁹⁹, 11186, F₃, 3, 15) (dual of [(11186, 3), 33459, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(3⁹⁹, 11186, F₃, 15) (dual of [11186, 11087, 16]-code), using

discarding factors / shortening the dual code based on linear OA(3⁹⁹, 19694, F₃, 15) (dual of [19694, 19595, 16]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(3⁹, 12, F₃, 7) (dual of [12, 3, 8]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁰, 13, F₃, 8) (dual of [13, 3, 9]-code), using
      - Simplex code S(3,3) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 13Â | 3³âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−1,0,…,6}|+1Â =Â 9 (BCH-bound) [i]
  2. linear OA(3⁹⁰, 19682, F₃, 15) (dual of [19682, 19592, 16]-code), using
    - 1 times truncation [i] based on linear OA(3⁹¹, 19683, F₃, 16) (dual of [19683, 19592, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(3⁹⁹, 5593, F₃, 5, 15) (dual of [(5593, 5), 27866, 16]-NRT-code)	[i]		OOA Folding