MinT - Information on Result #2642057

Information on Result #2642057

Linear OOA(7⁶⁵, large, F₇, 3, 3), using strength reduction based on linear OOA(7⁶⁵, large, F₇, 3, 6), using

(u,Â u+v)-construction [i] based on
1. linear OOA(7¹³, 6120101, F₇, 3, 3) (dual of [(6120101, 3), 18360290, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(7¹³, 6120101, F₇, 2, 3) (dual of [(6120101, 2), 12240189, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7¹³, 6120101, F₇, 3) (dual of [6120101, 6120088, 4]-code or 6120101-cap in PG(12,7)), using
      - product of projective cap with cap in AG(6,Â 7) [i] based on linear OA(7⁷, 2499, F₇, 3) (dual of [2499, 2492, 4]-code or 2499-cap in PG(6,7)), using
        product of two caps with tangent hyperplane [i]
2. linear OOA(7⁵², 5592402, F₇, 3, 6) (dual of [(5592402, 3), 16777154, 7]-NRT-code), using
  - trace code [i] based on linear OOA(49²⁶, 2796201, F₄₉, 3, 6) (dual of [(2796201, 3), 8388577, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(49²⁶, large, F₄₉, 6) (dual of [large, large−26, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 25679568Â | 49⁵âˆ’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(7⁶⁶, large, F₇, 3, 3)	[i]		OOA Duplication
2	Linear OOA(7⁶⁷, large, F₇, 3, 3)	[i]		OOA Duplication