MinT - Information on Result #896181

Information on Result #896181

Linear OOA(5¹³⁰, 4194405, F₅, 2, 14) (dual of [(4194405, 2), 8388680, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁹, 104, F₅, 2, 7) (dual of [(104, 2), 189, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁵, 66, F₅, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁵, 66, F₅, 3) (dual of [66, 61, 4]-code or 66-cap in PG(4,5)), using
      - caps completed using a computer search [i]
  2. linear OOA(5¹⁴, 52, F₅, 2, 7) (dual of [(52, 2), 90, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 52)-net over F₅, using
      - trace code for nets [i] based on digital (0, 7, 26)-net over F₂₅, using
        net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
        Niederreiter sequence [i]
linear OOA(5¹¹¹, 4194301, F₅, 2, 14) (dual of [(4194301, 2), 8388491, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹¹¹, 8388602, F₅, 14) (dual of [8388602, 8388491, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹¹¹, large, F₅, 14) (dual of [large, large−111, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.

Other Results with Identical Parameters

None.

Depending Results

None.