MinT - Information on Result #2648313

Information on Result #2648313

Linear OOA(49⁴⁵, large, F₄₉, 3, 3), using strength reduction based on linear OOA(49⁴⁵, large, F₄₉, 3, 7), using

(u,Â u+v)-construction [i] based on
1. linear OOA(49⁷, 5769603, F₄₉, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(49⁷, 5769603, F₄₉, 2, 3) (dual of [(5769603, 2), 11539199, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(49⁷, 5769603, F₄₉, 3) (dual of [5769603, 5769596, 4]-code or 5769603-cap in PG(6,49)), using
      - product of two caps with tangent hyperplane [i]
2. linear OOA(49³⁸, 5592402, F₄₉, 3, 7) (dual of [(5592402, 3), 16777168, 8]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(49⁷, 5769603, F₄₉, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code) (see above)
    2. 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.