MinT - Information on Result #1189826

Information on Result #1189826

Digital (52, 59, 3864756)-net over F₇, using net defined by OOA based on linear OOA(7⁵⁹, 3864756, F₇, 9, 7) (dual of [(3864756, 9), 34782745, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(7⁵⁹, 3864757, F₇, 3, 7) (dual of [(3864757, 3), 11594212, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁹, 21555, F₇, 3, 3) (dual of [(21555, 3), 64656, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(7⁹, 21555, F₇, 2, 3) (dual of [(21555, 2), 43101, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁹, 21555, F₇, 3) (dual of [21555, 21546, 4]-code or 21555-cap in PG(8,7)), using
        caps completed using a computer search [i]
  2. linear OOA(7⁵⁰, 3843202, F₇, 3, 7) (dual of [(3843202, 3), 11529556, 8]-NRT-code), using
    - trace code [i] based on linear OOA(49²⁵, 1921601, F₄₉, 3, 7) (dual of [(1921601, 3), 5764778, 8]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(49²⁵, 5764803, F₄₉, 7) (dual of [5764803, 5764778, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(49²⁵, 5764805, F₄₉, 7) (dual of [5764805, 5764780, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(49²⁵, 5764801, F₄₉, 7) (dual of [5764801, 5764776, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(49²¹, 5764801, F₄₉, 6) (dual of [5764801, 5764780, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.