MinT - Information on Result #1193050

Information on Result #1193050

Digital (19, 25, 4384)-net over F₉, using net defined by OOA based on linear OOA(9²⁵, 4384, F₉, 9, 6) (dual of [(4384, 9), 39431, 7]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(9²⁵, 4385, F₉, 3, 6) (dual of [(4385, 3), 13130, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9³, 10, F₉, 3, 3) (dual of [(10, 3), 27, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;27,9) [i]
  2. linear OOA(9²², 4375, F₉, 3, 6) (dual of [(4375, 3), 13103, 7]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(9²², 13125, F₉, 6) (dual of [13125, 13103, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(9²², 13126, F₉, 6) (dual of [13126, 13104, 7]-code), using
        trace code [i] based on linear OA(81¹¹, 6563, F₈₁, 6) (dual of [6563, 6552, 7]-code), using
        constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        linear OA(81¹¹, 6561, F₈₁, 6) (dual of [6561, 6550, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(81⁹, 6561, F₈₁, 5) (dual of [6561, 6552, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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.