MinT - Information on Result #1191724

Information on Result #1191724

Digital (115, 128, 2801695)-net over F₈, using net defined by OOA based on linear OOA(8¹²⁸, 2801695, F₈, 15, 13) (dual of [(2801695, 15), 42025297, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(8¹²⁸, 5603391, F₈, 3, 13) (dual of [(5603391, 3), 16810045, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8³⁰, 10989, F₈, 3, 6) (dual of [(10989, 3), 32937, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(8⁴, 65, F₈, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(8⁴, 65, F₈, 2, 3) (dual of [(65, 2), 126, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
        ovoid in PG(3,Â 8) [i]
      2. linear OOA(8²⁶, 10924, F₈, 3, 6) (dual of [(10924, 3), 32746, 7]-NRT-code), using
        OOA 3-folding [i] based on linear OA(8²⁶, 32772, F₈, 6) (dual of [32772, 32746, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(8²⁶, 32773, F₈, 6) (dual of [32773, 32747, 7]-code), using
        constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        linear OA(8²⁶, 32768, F₈, 6) (dual of [32768, 32742, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(8²¹, 32768, F₈, 5) (dual of [32768, 32747, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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(8⁹⁸, 5592402, F₈, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
    - trace code [i] based on linear OOA(64⁴⁹, 2796201, F₆₄, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’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.