MinT - Information on Result #1191888

Information on Result #1191888

Digital (146, 161, 2097173)-net over F₈, using net defined by OOA based on linear OOA(8¹⁶¹, 2097173, F₈, 21, 15) (dual of [(2097173, 21), 44040472, 16]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(8¹⁶¹, 6291520, F₈, 3, 15) (dual of [(6291520, 3), 18874399, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁴⁷, 699118, F₈, 3, 7) (dual of [(699118, 3), 2097307, 8]-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(8⁴³, 699053, F₈, 3, 7) (dual of [(699053, 3), 2097116, 8]-NRT-code), using
        OOA 3-folding [i] based on linear OA(8⁴³, 2097159, F₈, 7) (dual of [2097159, 2097116, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(8⁴³, 2097152, F₈, 7) (dual of [2097152, 2097109, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(8³⁶, 2097152, F₈, 6) (dual of [2097152, 2097116, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 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(8¹¹⁴, 5592402, F₈, 3, 15) (dual of [(5592402, 3), 16777092, 16]-NRT-code), using
    - trace code [i] based on linear OOA(64⁵⁷, 2796201, F₆₄, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64⁵⁷, large, F₆₄, 15) (dual of [large, large−57, 16]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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.