MinT - Information on Result #1013159

Information on Result #1013159

Linear OOA(5¹⁰⁶, 2796267, F₅, 3, 12) (dual of [(2796267, 3), 8388695, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁵, 66, F₅, 3, 6) (dual of [(66, 3), 183, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁵, 66, F₅, 3, 3) (dual of [(66, 3), 193, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(5⁵, 66, F₅, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁵, 66, F₅, 3) (dual of [66, 61, 4]-code or 66-cap in PG(4,5)), using
        caps completed using a computer search [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(5⁹¹, 2796201, F₅, 3, 12) (dual of [(2796201, 3), 8388512, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁹¹, large, F₅, 12) (dual of [large, large−91, 13]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’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(5¹⁰⁶, 1398133, F₅, 15, 12) (dual of [(1398133, 15), 20971889, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row