MinT - Information on Result #2704877

Information on Result #2704877

Linear OOA(49⁴¹, large, F₄₉, 3, 4), using 49¹ times duplication based on linear OOA(49⁴⁰, large, F₄₉, 3, 4), using

strength reduction [i] based on linear OOA(49⁴⁰, large, F₄₉, 3, 6), 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(49³³, 5592402, F₄₉, 3, 6) (dual of [(5592402, 3), 16777173, 7]-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(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

None.