MinT - Information on Result #1200604

Information on Result #1200604

Digital (19, 31, 426)-net over F₄₉, using net defined by OOA based on linear OOA(49³¹, 426, F₄₉, 15, 12) (dual of [(426, 15), 6359, 13]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(49³¹, 853, F₄₉, 3, 12) (dual of [(853, 3), 2528, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49⁸, 52, F₄₉, 3, 6) (dual of [(52, 3), 148, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 8, 52)-net over F₄₉, using
      - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. linear OOA(49²³, 801, F₄₉, 3, 12) (dual of [(801, 3), 2380, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(49²³, 2403, F₄₉, 12) (dual of [2403, 2380, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(49²³, 2401, F₄₉, 12) (dual of [2401, 2378, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(49²¹, 2401, F₄₉, 11) (dual of [2401, 2380, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(49⁰, 2, F₄₉, 0) (dual of [2, 2, 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.