MinT - Information on Result #1196530

Information on Result #1196530

Digital (41, 58, 1960)-net over F₂₅, using net defined by OOA based on linear OOA(25⁵⁸, 1960, F₂₅, 18, 17) (dual of [(1960, 18), 35222, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(25⁵⁸, 7841, F₂₅, 2, 17) (dual of [(7841, 2), 15624, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁹, 27, F₂₅, 2, 8) (dual of [(27, 2), 45, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 9, 27)-net over F₂₅, using
      - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
        Niederreiter sequence [i]
  2. linear OOA(25⁴⁹, 7814, F₂₅, 2, 17) (dual of [(7814, 2), 15579, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁴⁹, 15628, F₂₅, 17) (dual of [15628, 15579, 18]-code), using
      - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
        linear OA(25⁴⁹, 15625, F₂₅, 17) (dual of [15625, 15576, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(25⁴⁶, 15625, F₂₅, 16) (dual of [15625, 15579, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(25⁰, 3, F₂₅, 0) (dual of [3, 3, 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.