MinT - Information on Result #1599603

Information on Result #1599603

Linear OOA(2²⁴⁷, 1363, F₂, 4, 41) (dual of [(1363, 4), 5205, 42]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁷, 1363, F₂, 3, 41) (dual of [(1363, 3), 3842, 42]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁷, 1375, F₂, 3, 41) (dual of [(1375, 3), 3878, 42]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²⁴⁷, 4125, F₂, 41) (dual of [4125, 3878, 42]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁴⁷, 4127, F₂, 41) (dual of [4127, 3880, 42]-code), using
    - constructionÂ X applied to C([0,20]) âŠ‚ C([0,18]) [i] based on
      1. linear OA(2²⁴¹, 4097, F₂, 41) (dual of [4097, 3856, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]
      2. linear OA(2²¹⁷, 4097, F₂, 37) (dual of [4097, 3880, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
      3. linear OA(2⁶, 30, F₂, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2²⁴⁷, 681, F₂, 7, 41) (dual of [(681, 7), 4520, 42]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴⁷, 681, F₂, 8, 41) (dual of [(681, 8), 5201, 42]-NRT-code)	[i]		OOA Folding