MinT - Information on Result #1084702

Information on Result #1084702

Linear OOA(3¹²⁷, 4194832, F₃, 4, 9) (dual of [(4194832, 4), 16779201, 10]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁹, 532, F₃, 4, 3) (dual of [(532, 4), 2119, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(3⁹, 532, F₃, 3, 3) (dual of [(532, 3), 1587, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(3⁹, 532, F₃, 2, 3) (dual of [(532, 2), 1055, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁹, 532, F₃, 3) (dual of [532, 523, 4]-code or 532-cap in PG(8,3)), 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(3¹²⁷, 4194831, F₃, 5, 9) (dual of [(4194831, 5), 20974028, 10]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3¹²⁷, 4194831, F₃, 12, 9) (dual of [(4194831, 12), 50337845, 10]-NRT-code)	[i]		OOA Stacking with Additional Row