MinT - Information on Result #1200802

Information on Result #1200802

Digital (39, 55, 14719)-net over F₄₉, using net defined by OOA based on linear OOA(49⁵⁵, 14719, F₄₉, 18, 16) (dual of [(14719, 18), 264887, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(49⁵⁵, 58877, F₄₉, 2, 16) (dual of [(58877, 2), 117699, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49⁹, 51, F₄₉, 2, 8) (dual of [(51, 2), 93, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 9, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. linear OOA(49⁴⁶, 58826, F₄₉, 2, 16) (dual of [(58826, 2), 117606, 17]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(49⁴⁶, 117652, F₄₉, 16) (dual of [117652, 117606, 17]-code), using
      - constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
        linear OA(49⁴⁶, 117649, F₄₉, 16) (dual of [117649, 117603, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(49⁴³, 117649, F₄₉, 15) (dual of [117649, 117606, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.