MinT - Information on Result #1193768

Information on Result #1193768

Digital (125, 138, 3593404)-net over F₉, using net defined by OOA based on linear OOA(9¹³⁸, 3593404, F₉, 15, 13) (dual of [(3593404, 15), 53900922, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(9¹³⁸, 7186809, F₉, 3, 13) (dual of [(7186809, 3), 21560289, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9⁴⁰, 1594407, F₉, 3, 6) (dual of [(1594407, 3), 4783181, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(9⁴, 82, F₉, 3, 3) (dual of [(82, 3), 242, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(9⁴, 82, F₉, 2, 3) (dual of [(82, 2), 160, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁴, 82, F₉, 3) (dual of [82, 78, 4]-code or 82-cap in PG(3,9)), using
        ovoid in PG(3,Â 9) [i]
      2. linear OOA(9³⁶, 1594325, F₉, 3, 6) (dual of [(1594325, 3), 4782939, 7]-NRT-code), using
        OOA 3-folding [i] based on linear OA(9³⁶, 4782975, F₉, 6) (dual of [4782975, 4782939, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(9³⁶, 4782976, F₉, 6) (dual of [4782976, 4782940, 7]-code), using
        constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        linear OA(9³⁶, 4782969, F₉, 6) (dual of [4782969, 4782933, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(9²⁹, 4782969, F₉, 5) (dual of [4782969, 4782940, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
  2. linear OOA(9⁹⁸, 5592402, F₉, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
    - trace code [i] based on linear OOA(81⁴⁹, 2796201, F₈₁, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.