MinT - Information on Result #1201562

Information on Result #1201562

Digital (69, 86, 1049788)-net over F₆₄, using net defined by OOA based on linear OOA(64⁸⁶, 1049788, F₆₄, 18, 17) (dual of [(1049788, 18), 18896098, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(64⁸⁶, 4199153, F₆₄, 2, 17) (dual of [(4199153, 2), 8398220, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁸⁶, 4199155, F₆₄, 2, 17) (dual of [(4199155, 2), 8398224, 18]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(64²¹, 4854, F₆₄, 2, 8) (dual of [(4854, 2), 9687, 9]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64²¹, 9708, F₆₄, 8) (dual of [9708, 9687, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(64²¹, 9709, F₆₄, 8) (dual of [9709, 9688, 9]-code), using
        the BCH-code C(I) with length 9709Â | 64³âˆ’1, defining interval IÂ =Â {1,10,19,…,64}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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 (155, 172, 2099576)-net over F₈	[i]		Trace Code for Nets