MinT - Information on Result #1195958

Information on Result #1195958

Digital (19, 27, 3920)-net over F₂₅, using net defined by OOA based on linear OOA(25²⁷, 3920, F₂₅, 10, 8) (dual of [(3920, 10), 39173, 9]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(25²⁷, 7841, F₂₅, 2, 8) (dual of [(7841, 2), 15655, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁵, 27, F₂₅, 2, 4) (dual of [(27, 2), 49, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 5, 27)-net over F₂₅, using
      - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
        Niederreiter sequence [i]
  2. linear OOA(25²², 7814, F₂₅, 2, 8) (dual of [(7814, 2), 15606, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25²², 15628, F₂₅, 8) (dual of [15628, 15606, 9]-code), using
      - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
        linear OA(25²², 15625, F₂₅, 8) (dual of [15625, 15603, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(25¹⁹, 15625, F₂₅, 7) (dual of [15625, 15606, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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.