MinT - Information on Result #1013218

Information on Result #1013218

Linear OOA(5¹¹⁵, 2796260, F₅, 3, 13) (dual of [(2796260, 3), 8388665, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁴, 59, F₅, 3, 6) (dual of [(59, 3), 163, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁴, 26, F₅, 3, 3) (dual of [(26, 3), 74, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(5⁴, 26, F₅, 2, 3) (dual of [(26, 2), 48, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
        ovoid in PG(3,Â 5) [i]
  2. linear OOA(5¹⁰, 33, F₅, 3, 6) (dual of [(33, 3), 89, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 10, 33)-net over F₅, using
      - linear code embedding found in a computer search [i]
linear OOA(5¹⁰¹, 2796201, F₅, 3, 13) (dual of [(2796201, 3), 8388502, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5¹⁰¹, large, F₅, 13) (dual of [large, large−101, 14]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹¹⁵, 1398129, F₅, 15, 13) (dual of [(1398129, 15), 20971820, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row