MinT - Information on Result #2702178

Information on Result #2702178

Linear OOA(9¹²⁹, large, F₉, 3, 6), using 25 times NRT-code embedding in larger space based on linear OOA(9⁵⁴, large, F₉, 3, 6), using

(u,Â u+v)-construction [i] based on
1. linear OOA(9¹², 5580100, F₉, 3, 3) (dual of [(5580100, 3), 16740288, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(9¹², 5580100, F₉, 2, 3) (dual of [(5580100, 2), 11160188, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9¹², 5580100, F₉, 3) (dual of [5580100, 5580088, 4]-code or 5580100-cap in PG(11,9)), using
      - product of projective cap with cap in AG(5,Â 9) [i] based on linear OA(9⁷, 6723, F₉, 3) (dual of [6723, 6716, 4]-code or 6723-cap in PG(6,9)), using
        product of two caps with tangent hyperplane [i]
2. linear OOA(9⁴², 5592402, F₉, 3, 6) (dual of [(5592402, 3), 16777164, 7]-NRT-code), using
  - trace code [i] based on linear OOA(81²¹, 2796201, F₈₁, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, 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(9¹³⁰, large, F₉, 3, 6)	[i]		OOA Duplication