MinT - Information on Result #1519454

Information on Result #1519454

Linear OOA(2²⁵², 1382, F₂, 3, 41) (dual of [(1382, 3), 3894, 42]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵², 1382, F₂, 2, 41) (dual of [(1382, 2), 2512, 42]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁵², 2066, F₂, 2, 41) (dual of [(2066, 2), 3880, 42]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2²⁴⁸, 2064, F₂, 2, 41) (dual of [(2064, 2), 3880, 42]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2²⁴⁸, 4128, F₂, 41) (dual of [4128, 3880, 42]-code), using
    - 1 times code embedding in larger space [i] 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
        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]
        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]
        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(2²⁵², 691, F₂, 6, 41) (dual of [(691, 6), 3894, 42]-NRT-code)	[i]		OOA Folding