MinT - Information on Result #1186580

Information on Result #1186580

Digital (137, 153, 1048577)-net over F₄, using net defined by OOA based on linear OOA(4¹⁵³, 1048577, F₄, 18, 16) (dual of [(1048577, 18), 18874233, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(4¹⁵³, 4194309, F₄, 2, 16) (dual of [(4194309, 2), 8388465, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁵³, 4194310, F₄, 2, 16) (dual of [(4194310, 2), 8388467, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(4⁹, 9, F₄, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,9P) [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(4¹⁴⁴, 4194301, F₄, 2, 16) (dual of [(4194301, 2), 8388458, 17]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(4¹⁴⁴, 8388602, F₄, 16) (dual of [8388602, 8388458, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁴⁴, large, F₄, 16) (dual of [large, large−144, 17]-code), using
        the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.