MinT - Information on Result #1202420

Information on Result #1202420

Digital (61, 74, 2796241)-net over F₈₁, using net defined by OOA based on linear OOA(81⁷⁴, 2796241, F₈₁, 15, 13) (dual of [(2796241, 15), 41943541, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(81⁷⁴, 5592483, F₈₁, 3, 13) (dual of [(5592483, 3), 16777375, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81⁷⁴, 5592484, F₈₁, 3, 13) (dual of [(5592484, 3), 16777378, 14]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(81⁴, 82, F₈₁, 3, 4) (dual of [(82, 3), 242, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;242,81) [i]
    2. linear OOA(81²¹, 2796201, F₈₁, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OOA(81⁴⁹, 2796201, F₈₁, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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 (135, 148, 5592482)-net over F₉	[i]		Trace Code for Nets