MinT - Information on Result #1639742

Information on Result #1639742

Linear OOA(2²⁵¹, 1502, F₂, 5, 40) (dual of [(1502, 5), 7259, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵¹, 1502, F₂, 2, 40) (dual of [(1502, 2), 2753, 41]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁵¹, 2065, F₂, 2, 40) (dual of [(2065, 2), 3879, 41]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²⁵⁰, 2065, F₂, 2, 40) (dual of [(2065, 2), 3880, 41]-NRT-code), using
  - 2 times NRT-code embedding in larger space [i] based on linear OOA(2²⁴⁶, 2063, F₂, 2, 40) (dual of [(2063, 2), 3880, 41]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2²⁴⁶, 4126, F₂, 40) (dual of [4126, 3880, 41]-code), using
      - 1 times truncation [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

None.