MinT - Information on Result #1192196

Information on Result #1192196

Digital (74, 93, 3649)-net over F₈, using net defined by OOA based on linear OOA(8⁹³, 3649, F₈, 21, 19) (dual of [(3649, 21), 76536, 20]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(8⁹³, 10948, F₈, 3, 19) (dual of [(10948, 3), 32751, 20]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8¹², 24, F₈, 3, 9) (dual of [(24, 3), 60, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,62P) [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(8⁸¹, 10924, F₈, 3, 19) (dual of [(10924, 3), 32691, 20]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(8⁸¹, 32772, F₈, 19) (dual of [32772, 32691, 20]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁸¹, 32773, F₈, 19) (dual of [32773, 32692, 20]-code), using
        constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
        linear OA(8⁸¹, 32768, F₈, 19) (dual of [32768, 32687, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(8⁷⁶, 32768, F₈, 18) (dual of [32768, 32692, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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]

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.