MinT - Information on Result #1180786

Information on Result #1180786

Digital (165, 179, 1198411)-net over F₂, using net defined by OOA based on linear OOA(2¹⁷⁹, 1198411, F₂, 21, 14) (dual of [(1198411, 21), 25166452, 15]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹⁷⁹, 1198412, F₂, 7, 14) (dual of [(1198412, 7), 8388705, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁸, 41, F₂, 7, 7) (dual of [(41, 7), 269, 8]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁸, 41, F₂, 6, 7) (dual of [(41, 6), 228, 8]-NRT-code), using
      - extracting embedded OOA [i] based on digital (11, 18, 41)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶¹, 1198371, F₂, 7, 14) (dual of [(1198371, 7), 8388436, 15]-NRT-code), using
    - OOA 7-folding [i] based on linear OA(2¹⁶¹, 8388597, F₂, 14) (dual of [8388597, 8388436, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.