MinT - Information on Result #1017363

Information on Result #1017363

Linear OOA(49⁵³, 39317, F₄₉, 3, 15) (dual of [(39317, 3), 117898, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49¹⁰, 100, F₄₉, 3, 7) (dual of [(100, 3), 290, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49³, 50, F₄₉, 3, 3) (dual of [(50, 3), 147, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;147,49) [i]
  2. linear OOA(49⁷, 50, F₄₉, 3, 7) (dual of [(50, 3), 143, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;143,49) [i]
linear OOA(49⁴³, 39217, F₄₉, 3, 15) (dual of [(39217, 3), 117608, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(49⁴³, 117651, F₄₉, 15) (dual of [117651, 117608, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(49⁴³, 117652, F₄₉, 15) (dual of [117652, 117609, 16]-code), using
    - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
      1. 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]
      2. 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]
      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.