MinT - Information on Result #1718798

Information on Result #1718798

Digital (171, 192, 1048577)-net over F₄, using net defined by OOA based on linear OOA(4¹⁹², 1048577, F₄, 27, 21) (dual of [(1048577, 27), 28311387, 22]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(4¹⁹², 4194309, F₄, 3, 21) (dual of [(4194309, 3), 12582735, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁹², 4194310, F₄, 3, 21) (dual of [(4194310, 3), 12582738, 22]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁹², 4194310, F₄, 2, 21) (dual of [(4194310, 2), 8388428, 22]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(4¹¹, 9, F₄, 2, 10) (dual of [(9, 2), 7, 11]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
      2. linear OOA(4¹⁸¹, 4194301, F₄, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
        OOA 2-folding [i] based on linear OA(4¹⁸¹, 8388602, F₄, 21) (dual of [8388602, 8388421, 22]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁸¹, large, F₄, 21) (dual of [large, large−181, 22]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: 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.