MinT - Information on Result #1084706

Information on Result #1084706

Linear OOA(3¹³¹, 4207612, F₃, 4, 9) (dual of [(4207612, 4), 16830317, 10]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3¹³, 13312, F₃, 4, 3) (dual of [(13312, 4), 53235, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(3¹³, 13312, F₃, 3, 3) (dual of [(13312, 3), 39923, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(3¹³, 13312, F₃, 2, 3) (dual of [(13312, 2), 26611, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3¹³, 13312, F₃, 3) (dual of [13312, 13299, 4]-code or 13312-cap in PG(12,3)), using
      - caps completed using a computer search [i]
linear OOA(3²⁸, 2097150, F₃, 4, 4) (dual of [(2097150, 4), 8388572, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁸, 2391484, F₃, 4, 4) (dual of [(2391484, 4), 9565908, 5]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3²⁸, 2391485, F₃, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (24, 28, 2391485)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁹⁰, 2097150, F₃, 4, 9) (dual of [(2097150, 4), 8388510, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3⁹⁰, 8388600, F₃, 9) (dual of [8388600, 8388510, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁹⁰, large, F₃, 9) (dual of [large, large−90, 10]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹³¹, 4207611, F₃, 5, 9) (dual of [(4207611, 5), 21037924, 10]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3¹³¹, 4207611, F₃, 12, 9) (dual of [(4207611, 12), 50491201, 10]-NRT-code)	[i]		OOA Stacking with Additional Row