MinT - Information on Result #1825538

Information on Result #1825538

(41, 64, 5958)-net in base 64, using base change based on digital (25, 48, 5958)-net over F₂₅₆, using

256² times duplication [i] based on digital (23, 46, 5958)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256⁴⁶, 5958, F₂₅₆, 23, 23) (dual of [(5958, 23), 136988, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(256⁴⁶, 65539, F₂₅₆, 23) (dual of [65539, 65493, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(256⁴⁶, 65542, F₂₅₆, 23) (dual of [65542, 65496, 24]-code), using
      - constructionÂ X applied to C([0,11]) âŠ‚ C([0,10]) [i] based on
        linear OA(256⁴⁵, 65537, F₂₅₆, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
        linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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	(42, 65, 5958)-net in base 64	[i]		Net Duplication