MinT - Information on Result #1705147

Information on Result #1705147

Linear OOA(2²³⁷, 2099880, F₂, 8, 17) (dual of [(2099880, 8), 16798803, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁷, 2099880, F₂, 4, 17) (dual of [(2099880, 4), 8399283, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵², 2730, F₂, 4, 8) (dual of [(2730, 4), 10868, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁵², 2730, F₂, 3, 8) (dual of [(2730, 3), 8138, 9]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2⁵², 8190, F₂, 8) (dual of [8190, 8138, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁵², 8192, F₂, 8) (dual of [8192, 8140, 9]-code), using
        1 times truncation [i] based on linear OA(2⁵³, 8193, F₂, 9) (dual of [8193, 8140, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’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, 2097150, F₂, 4, 17) (dual of [(2097150, 4), 8388415, 18]-NRT-code), using
  - OOA 4-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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²³⁷, 2099879, F₂, 24, 17) (dual of [(2099879, 24), 50396859, 18]-NRT-code)	[i]		OOA Stacking with Additional Row