MinT - Information on Result #1165823

Information on Result #1165823

Linear OOA(2²⁵⁷, 1048589, F₂, 8, 21) (dual of [(1048589, 8), 8388455, 22]-NRT-code), using OOA 2-folding based on linear OOA(2²⁵⁷, 2097178, F₂, 4, 21) (dual of [(2097178, 4), 8388455, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁵⁷, 2097179, F₂, 4, 21) (dual of [(2097179, 4), 8388459, 22]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁶, 29, F₂, 4, 10) (dual of [(29, 4), 90, 11]-NRT-code), using
    - extracting embedded OOA [i] based on digital (16, 26, 29)-net over F₂, using
      - 3 times m-reduction [i] based on digital (16, 29, 29)-net over F₂, using
        a shift-net [i]
  2. linear OOA(2²³¹, 2097150, F₂, 4, 21) (dual of [(2097150, 4), 8388369, 22]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2²³¹, 8388600, F₂, 21) (dual of [8388600, 8388369, 22]-code), using
      - discarding factors / shortening the dual code based on linear OA(2²³¹, large, F₂, 21) (dual of [large, large−231, 22]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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.

Other Results with Identical Parameters

None.

Depending Results

None.