MinT - Information on Result #1229494

Information on Result #1229494

Digital (123, 134, 3630904)-net over F₅, using generalized (u,Â u+v)-construction based on

digital (11, 14, 976592)-net over F₅, using
- s-reduction based on digital (11, 14, 1123200)-net over F₅, using
  - net defined by OOA [i] based on linear OOA(5¹⁴, 1123200, F₅, 3, 3) (dual of [(1123200, 3), 3369586, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(5¹⁴, 1123200, F₅, 2, 3) (dual of [(1123200, 2), 2246386, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5¹⁴, 1123200, F₅, 3) (dual of [1123200, 1123186, 4]-code or 1123200-cap in PG(13,5)), using
        product of two projective caps and an affine cap avoiding two hyperplanes [i] based on
        linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
        ovoid in PG(3,Â 5) [i]
        linear OA(5⁷, 675, F₅, 3) (dual of [675, 668, 4]-code or 675-cap in PG(6,5)), using
        product of two caps with tangent hyperplane [i]
digital (34, 39, 976592)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5³⁹, 976592, F₅, 6, 5) (dual of [(976592, 6), 5859513, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(5³⁹, 976593, F₅, 2, 5) (dual of [(976593, 2), 1953147, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
        appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
        Hamming code H(3,5) [i]
      2. linear OOA(5³⁶, 976562, F₅, 2, 5) (dual of [(976562, 2), 1953088, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(5³⁶, 1953124, F₅, 5) (dual of [1953124, 1953088, 6]-code), using
        1 times truncation [i] based on linear OA(5³⁷, 1953125, F₅, 6) (dual of [1953125, 1953088, 7]-code), using
        an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
digital (70, 81, 1677720)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁸¹, 1677720, F₅, 11, 11) (dual of [(1677720, 11), 18454839, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(5⁸¹, 8388601, F₅, 11) (dual of [8388601, 8388520, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.