MinT - Information on Result #1718000

Information on Result #1718000

Digital (94, 109, 63222)-net over F₄, using net defined by OOA based on linear OOA(4¹⁰⁹, 63222, F₄, 21, 15) (dual of [(63222, 21), 1327553, 16]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(4¹⁰⁹, 189667, F₄, 3, 15) (dual of [(189667, 3), 568892, 16]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁰⁹, 189667, F₄, 15) (dual of [189667, 189558, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁰⁹, 262161, F₄, 15) (dual of [262161, 262052, 16]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(4⁹, 17, F₄, 7) (dual of [17, 8, 8]-code), using
        dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(4⁸, 17, F₄, 6) (dual of [17, 9, 7]-code), using
        the BCH-code C(I) with length 17Â | 4⁴âˆ’1, defining interval IÂ =Â {1,4,7,…,16}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        nonexistence of linear OA(4⁷, 10, F₄, 6) (dual of [10, 3, 7]-code), because
        bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
      2. linear OA(4¹⁰⁰, 262144, F₄, 15) (dual of [262144, 262044, 16]-code), using
        an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: 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.