MinT - Information on Result #903299

Information on Result #903299

Linear OOA(49⁵¹, 58927, F₄₉, 2, 14) (dual of [(58927, 2), 117803, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49¹¹, 101, F₄₉, 2, 7) (dual of [(101, 2), 191, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49³, 50, F₄₉, 2, 3) (dual of [(50, 2), 97, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;97,49) [i]
  2. linear OOA(49⁸, 51, F₄₉, 2, 7) (dual of [(51, 2), 94, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 8, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
linear OOA(49⁴⁰, 58826, F₄₉, 2, 14) (dual of [(58826, 2), 117612, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(49⁴⁰, 117652, F₄₉, 14) (dual of [117652, 117612, 15]-code), using
  - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
    1. linear OA(49⁴⁰, 117649, F₄₉, 14) (dual of [117649, 117609, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    2. linear OA(49³⁷, 117649, F₄₉, 13) (dual of [117649, 117612, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.