MinT - Information on Result #1202588

Information on Result #1202588

Digital (58, 74, 1048665)-net over F₈₁, using net defined by OOA based on linear OOA(81⁷⁴, 1048665, F₈₁, 20, 16) (dual of [(1048665, 20), 20973226, 17]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(81⁷⁴, 2097331, F₈₁, 4, 16) (dual of [(2097331, 4), 8389250, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81⁷⁴, 2097332, F₈₁, 4, 16) (dual of [(2097332, 4), 8389254, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(81¹³, 182, F₈₁, 4, 8) (dual of [(182, 4), 715, 9]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(81⁴, 82, F₈₁, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;324,81) [i]
        linear OOA(81⁹, 100, F₈₁, 4, 8) (dual of [(100, 4), 391, 9]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,391P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
    2. linear OOA(81⁶¹, 2097150, F₈₁, 4, 16) (dual of [(2097150, 4), 8388539, 17]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(81⁶¹, 8388600, F₈₁, 16) (dual of [8388600, 8388539, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁶¹, large, F₈₁, 16) (dual of [large, large−61, 17]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,15], 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

The following results depend on this result:

	Result		This result only	Method
1	Digital (132, 148, 2097330)-net over F₉	[i]		Trace Code for Nets