MinT - Information on Result #1150822

Information on Result #1150822

Linear OOA(2²¹⁹, 2796283, F₂, 7, 13) (dual of [(2796283, 7), 19573762, 14]-NRT-code), using OOA stacking with additional row based on linear OOA(2²¹⁹, 2796284, F₂, 6, 13) (dual of [(2796284, 6), 16777485, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁴, 2097149, F₂, 6, 6) (dual of [(2097149, 6), 12582830, 7]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁶⁴, 2097150, F₂, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
    - 1 step truncation [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁵⁵, 1398142, F₂, 6, 13) (dual of [(1398142, 6), 8388697, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹⁶, 42, F₂, 6, 6) (dual of [(42, 6), 236, 7]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹⁶, 42, F₂, 5, 6) (dual of [(42, 5), 194, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (10, 16, 42)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2¹³⁹, 1398100, F₂, 6, 13) (dual of [(1398100, 6), 8388461, 14]-NRT-code), using
      - OOA 6-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.