MinT - Information on Result #895087

Information on Result #895087

Linear OOA(3¹⁵⁴, 4194347, F₃, 2, 14) (dual of [(4194347, 2), 8388540, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁸, 46, F₃, 2, 7) (dual of [(46, 2), 74, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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(3¹³, 26, F₃, 2, 7) (dual of [(26, 2), 39, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 13, 26)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹³⁶, 4194301, F₃, 2, 14) (dual of [(4194301, 2), 8388466, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹³⁶, 8388602, F₃, 14) (dual of [8388602, 8388466, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹³⁶, large, F₃, 14) (dual of [large, large−136, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁵⁴, 2097173, F₃, 4, 14) (dual of [(2097173, 4), 8388538, 15]-NRT-code)	[i]		OOA Folding