MinT - Information on Result #1117506

Information on Result #1117506

Linear OOA(3¹⁵⁶, 1677788, F₃, 5, 14) (dual of [(1677788, 5), 8388784, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²⁰, 68, F₃, 5, 7) (dual of [(68, 5), 320, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 56, F₃, 5, 3) (dual of [(56, 5), 274, 4]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3⁶, 56, F₃, 3, 3) (dual of [(56, 3), 162, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁶, 56, F₃, 2, 3) (dual of [(56, 2), 106, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
  2. linear OOA(3¹⁴, 34, F₃, 5, 7) (dual of [(34, 5), 156, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 34)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹³⁶, 1677720, F₃, 5, 14) (dual of [(1677720, 5), 8388464, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹³⁶, 8388600, F₃, 14) (dual of [8388600, 8388464, 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(3²⁴⁵, 5033364, F₃, 5, 14) (dual of [(5033364, 5), 25166575, 15]-NRT-code)	[i]		Generalized (u,Â u+v)-Construction for OOAs