MinT - Information on Result #1191530

Information on Result #1191530

Digital (68, 80, 349538)-net over F₈, using net defined by OOA based on linear OOA(8⁸⁰, 349538, F₈, 15, 12) (dual of [(349538, 15), 5242990, 13]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(8⁸⁰, 699077, F₈, 3, 12) (dual of [(699077, 3), 2097151, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁹, 24, F₈, 3, 6) (dual of [(24, 3), 63, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,65P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]
  2. linear OOA(8⁷¹, 699053, F₈, 3, 12) (dual of [(699053, 3), 2097088, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(8⁷¹, 2097159, F₈, 12) (dual of [2097159, 2097088, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(8⁷¹, 2097152, F₈, 12) (dual of [2097152, 2097081, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(8⁶⁴, 2097152, F₈, 11) (dual of [2097152, 2097088, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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]

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.