MinT - Information on Result #1600649

Information on Result #1600649

Linear OOA(2²⁵⁷, 2883582, F₂, 4, 17) (dual of [(2883582, 4), 11534071, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵⁷, 2883582, F₂, 3, 17) (dual of [(2883582, 3), 8650489, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁷², 87381, F₂, 3, 8) (dual of [(87381, 3), 262071, 9]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁷², 262143, F₂, 8) (dual of [262143, 262071, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁷², 262144, F₂, 8) (dual of [262144, 262072, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁷³, 262145, F₂, 9) (dual of [262145, 262072, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 262145Â | 2³⁶âˆ’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, 2796201, F₂, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
  - OOA 3-folding [i] 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁵⁷, 1441791, F₂, 7, 17) (dual of [(1441791, 7), 10092280, 18]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁵⁷, 1441791, F₂, 8, 17) (dual of [(1441791, 8), 11534071, 18]-NRT-code)	[i]		OOA Folding