MinT - Information on Result #1648977

Information on Result #1648977

Linear OOA(3²¹⁰, 4194432, F₃, 5, 19) (dual of [(4194432, 5), 20971950, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁰, 4194432, F₃, 2, 19) (dual of [(4194432, 2), 8388654, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁹, 131, F₃, 2, 9) (dual of [(131, 2), 233, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁹, 131, F₃, 9) (dual of [131, 102, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁹, 140, F₃, 9) (dual of [140, 111, 10]-code), using
      - a â€œBZâ€ code from Brouwerâ€™s database [i]
2. linear OOA(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(3²¹⁰, 2097215, F₃, 25, 19) (dual of [(2097215, 25), 52430165, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row