MinT - Information on Result #1718396

Information on Result #1718396

Digital (149, 167, 1398103)-net over F₄, using net defined by OOA based on linear OOA(4¹⁶⁷, 1398103, F₄, 21, 18) (dual of [(1398103, 21), 29359996, 19]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(4¹⁶⁷, 4194310, F₄, 3, 18) (dual of [(4194310, 3), 12582763, 19]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁶⁷, 4194310, F₄, 2, 18) (dual of [(4194310, 2), 8388453, 19]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(4¹⁰, 9, F₄, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,8P) [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(4¹⁵⁷, 4194301, F₄, 2, 18) (dual of [(4194301, 2), 8388445, 19]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(4¹⁵⁷, 8388602, F₄, 18) (dual of [8388602, 8388445, 19]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁵⁷, large, F₄, 18) (dual of [large, large−157, 19]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.