MinT - Information on Result #1189792

Information on Result #1189792

Digital (34, 41, 78441)-net over F₇, using net defined by OOA based on linear OOA(7⁴¹, 78441, F₇, 9, 7) (dual of [(78441, 9), 705928, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(7⁴¹, 78442, F₇, 3, 7) (dual of [(78442, 3), 235285, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7³, 8, F₇, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;21,7) [i]
  2. linear OOA(7³⁸, 78434, F₇, 3, 7) (dual of [(78434, 3), 235264, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(7³⁸, 235302, F₇, 7) (dual of [235302, 235264, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(7³⁸, 235304, F₇, 7) (dual of [235304, 235266, 8]-code), using
        trace code [i] based on linear OA(49¹⁹, 117652, F₄₉, 7) (dual of [117652, 117633, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(49¹⁹, 117649, F₄₉, 7) (dual of [117649, 117630, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(49¹⁶, 117649, F₄₉, 6) (dual of [117649, 117633, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(49⁰, 3, F₄₉, 0) (dual of [3, 3, 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.