MinT - Information on Result #1201550

Information on Result #1201550

Digital (61, 78, 1048611)-net over F₆₄, using net defined by OOA based on linear OOA(64⁷⁸, 1048611, F₆₄, 18, 17) (dual of [(1048611, 18), 18874920, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(64⁷⁸, 4194445, F₆₄, 2, 17) (dual of [(4194445, 2), 8388812, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁷⁸, 4194446, F₆₄, 2, 17) (dual of [(4194446, 2), 8388814, 18]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(64¹³, 145, F₆₄, 2, 8) (dual of [(145, 2), 277, 9]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(64⁴, 65, F₆₄, 2, 4) (dual of [(65, 2), 126, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;126,64) [i]
        linear OOA(64⁹, 80, F₆₄, 2, 8) (dual of [(80, 2), 151, 9]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,151P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
    2. linear OOA(64⁶⁵, 4194301, F₆₄, 2, 17) (dual of [(4194301, 2), 8388537, 18]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64⁶⁵, 8388602, F₆₄, 17) (dual of [8388602, 8388537, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁶⁵, large, F₆₄, 17) (dual of [large, large−65, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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

The following results depend on this result:

	Result		This result only	Method
1	Digital (139, 156, 2097222)-net over F₈	[i]		Trace Code for Nets