MinT - Information on Result #2697308

Information on Result #2697308

Linear OOA(7⁷⁷, large, F₇, 3, 6), using 7² times duplication based on linear OOA(7⁷⁵, large, F₇, 3, 6), using

strength reduction [i] based on linear OOA(7⁷⁵, large, F₇, 3, 7), 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(7⁶², 5592402, F₇, 3, 7) (dual of [(5592402, 3), 16777144, 8]-NRT-code), using
    - trace code [i] based on linear OOA(49³¹, 2796201, F₄₉, 3, 7) (dual of [(2796201, 3), 8388572, 8]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(49³¹, large, F₄₉, 7) (dual of [large, large−31, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 28247525Â | 49¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [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

None.