MinT - Information on Result #1010642

Information on Result #1010642

Linear OOA(3¹⁷⁹, 5592455, F₃, 3, 12) (dual of [(5592455, 3), 16777186, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁷, 53, F₃, 3, 6) (dual of [(53, 3), 142, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
        doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
  2. linear OOA(3¹², 33, F₃, 3, 6) (dual of [(33, 3), 87, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 12, 33)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁶², 5592402, F₃, 3, 12) (dual of [(5592402, 3), 16777044, 13]-NRT-code), using
- trace code [i] based on linear OOA(9⁸¹, 2796201, F₉, 3, 12) (dual of [(2796201, 3), 8388522, 13]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(9⁸¹, large, F₉, 12) (dual of [large, large−81, 13]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 9⁸âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁷⁹, 2796227, F₃, 5, 12) (dual of [(2796227, 5), 13980956, 13]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁷⁹, 2796227, F₃, 15, 12) (dual of [(2796227, 15), 41943226, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row