MinT - Information on Result #1200438

Information on Result #1200438

Digital (21, 30, 29438)-net over F₄₉, using net defined by OOA based on linear OOA(49³⁰, 29438, F₄₉, 10, 9) (dual of [(29438, 10), 294350, 10]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(49³⁰, 58877, F₄₉, 2, 9) (dual of [(58877, 2), 117724, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49⁵, 51, F₄₉, 2, 4) (dual of [(51, 2), 97, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 5, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. linear OOA(49²⁵, 58826, F₄₉, 2, 9) (dual of [(58826, 2), 117627, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(49²⁵, 117652, F₄₉, 9) (dual of [117652, 117627, 10]-code), using
      - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
        linear OA(49²⁵, 117649, F₄₉, 9) (dual of [117649, 117624, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(49²², 117649, F₄₉, 8) (dual of [117649, 117627, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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.