MinT - Information on Result #1841361

Information on Result #1841361

(31, 40, 2101214)-net in base 64, using net defined by OOA based on OOA(64⁴⁰, 2101214, S₆₄, 10, 9), using

OOA 2-folding and stacking with additional row [i] based on OOA(64⁴⁰, 4202429, S₆₄, 2, 9), using
- (u,Â u+v)-construction [i] based on
  1. OOA(64⁷, 8128, S₆₄, 2, 4), using
    - OOA 2-folding [i] based on OA(64⁷, 16256, S₆₄, 4), using
      - discarding parts of the base [i] based on linear OA(128⁶, 16256, F₁₂₈, 4) (dual of [16256, 16250, 5]-code), using
        1 times truncation [i] based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OOA(64³³, 4194301, F₆₄, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(64³³, 8388602, F₆₄, 9) (dual of [8388602, 8388569, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(64³³, large, F₆₄, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive.

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	(71, 80, 4202428)-net in base 8	[i]		Trace Code for Nets