MinT - Information on Result #1201552

Information on Result #1201552

Digital (62, 79, 1048631)-net over F₆₄, using net defined by OOA based on linear OOA(64⁷⁹, 1048631, F₆₄, 18, 17) (dual of [(1048631, 18), 18875279, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(64⁷⁹, 4194525, F₆₄, 2, 17) (dual of [(4194525, 2), 8388971, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁷⁹, 4194528, F₆₄, 2, 17) (dual of [(4194528, 2), 8388977, 18]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(64¹⁴, 227, F₆₄, 2, 8) (dual of [(227, 2), 440, 9]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64¹⁴, 454, F₆₄, 8) (dual of [454, 440, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹⁴, 455, F₆₄, 8) (dual of [455, 441, 9]-code), using
        the BCH-code C(I) with length 455Â | 64²âˆ’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 (141, 158, 2097262)-net over F₈	[i]		Trace Code for Nets