MinT - Information on Result #895259

Information on Result #895259

Linear OOA(3²⁰⁰, 4194327, F₃, 2, 19) (dual of [(4194327, 2), 8388454, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁹, 26, F₃, 2, 9) (dual of [(26, 2), 33, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 14, F₃, 2, 4) (dual of [(14, 2), 22, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 6, 14)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹³, 13, F₃, 2, 9) (dual of [(13, 2), 13, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 13, 13)-net over F₃, using
      - a shift-net [i]
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: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁰⁰, 2097163, F₃, 4, 19) (dual of [(2097163, 4), 8388452, 20]-NRT-code)	[i]		OOA Folding