MinT - Information on Result #1686055

Information on Result #1686055

Linear OOA(2²¹³, 1677784, F₂, 7, 17) (dual of [(1677784, 7), 11744275, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹³, 1677784, F₂, 5, 17) (dual of [(1677784, 5), 8388707, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²⁸, 64, F₂, 5, 8) (dual of [(64, 5), 292, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁸, 64, F₂, 2, 8) (dual of [(64, 2), 100, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2²⁸, 128, F₂, 8) (dual of [128, 100, 9]-code), using
      - 1 times truncation [i] based on linear OA(2²⁹, 129, F₂, 9) (dual of [129, 100, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 129Â | 2¹⁴âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
2. linear OOA(2¹⁸⁵, 1677720, F₂, 5, 17) (dual of [(1677720, 5), 8388415, 18]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2¹⁸⁵, 8388600, F₂, 17) (dual of [8388600, 8388415, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: 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.