MinT - Information on Result #1196294

Information on Result #1196294

Digital (42, 55, 65113)-net over F₂₅, using net defined by OOA based on linear OOA(25⁵⁵, 65113, F₂₅, 14, 13) (dual of [(65113, 14), 911527, 14]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(25⁵⁵, 195340, F₂₅, 2, 13) (dual of [(195340, 2), 390625, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁶, 26, F₂₅, 2, 6) (dual of [(26, 2), 46, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;46,25) [i]
  2. linear OOA(25⁴⁹, 195314, F₂₅, 2, 13) (dual of [(195314, 2), 390579, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁴⁹, 390628, F₂₅, 13) (dual of [390628, 390579, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁴⁹, 390629, F₂₅, 13) (dual of [390629, 390580, 14]-code), using
        constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(25⁴⁹, 390625, F₂₅, 13) (dual of [390625, 390576, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(25⁴⁵, 390625, F₂₅, 12) (dual of [390625, 390580, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(25⁰, 4, F₂₅, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 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.