MinT - Information on Result #2864787

Information on Result #2864787

Linear OOA(2¹⁸⁴, 1694102, F₂, 5, 13) (dual of [(1694102, 5), 8470326, 14]-NRT-code), using 2² times duplication based on linear OOA(2¹⁸², 1694102, F₂, 5, 13) (dual of [(1694102, 5), 8470328, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴³, 16382, F₂, 5, 6) (dual of [(16382, 5), 81867, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (37, 43, 16382)-net over F₂, using
    - 1 times m-reduction [i] based on digital (37, 44, 16382)-net over F₂, using
      - net defined by OOA [i] based on linear OOA(2⁴⁴, 16382, F₂, 7, 7) (dual of [(16382, 7), 114630, 8]-NRT-code), using
        OOA stacking with additional row [i] based on linear OOA(2⁴⁴, 16383, F₂, 3, 7) (dual of [(16383, 3), 49105, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
2. linear OOA(2¹³⁹, 1677720, F₂, 5, 13) (dual of [(1677720, 5), 8388461, 14]-NRT-code), using
  - OOA 5-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.