MinT - Information on Result #2768188

Information on Result #2768188

Linear OOA(2²⁵⁸, 4456442, F₂, 4, 12) (dual of [(4456442, 4), 17825510, 13]-NRT-code), using strength reduction based on linear OOA(2²⁵⁸, 4456442, F₂, 4, 13) (dual of [(4456442, 4), 17825510, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁷, 4194301, F₂, 4, 6) (dual of [(4194301, 4), 16777137, 7]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁶⁷, 4194302, F₂, 3, 6) (dual of [(4194302, 3), 12582839, 7]-NRT-code), using
    - 1 step truncation [i] based on linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁹¹, 2228221, F₂, 4, 13) (dual of [(2228221, 4), 8912693, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁵², 131071, F₂, 4, 6) (dual of [(131071, 4), 524232, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (46, 52, 131071)-net over F₂, using
        1 times m-reduction [i] based on digital (46, 53, 131071)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
    2. linear OOA(2¹³⁹, 2097150, F₂, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
      - OOA 4-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.