MinT - Information on Result #1832024

Information on Result #1832024

OOA(32⁶⁷, 4718591, S₃₂, 2, 11), using (u,Â u+v)-construction based on

linear OOA(32¹⁷, 524290, F₃₂, 2, 5) (dual of [(524290, 2), 1048563, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹⁷, 1048580, F₃₂, 5) (dual of [1048580, 1048563, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. linear OA(32¹⁷, 1048576, F₃₂, 5) (dual of [1048576, 1048559, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OA(32¹³, 1048576, F₃₂, 4) (dual of [1048576, 1048563, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
OOA(32⁵⁰, 4194301, S₃₂, 2, 11), using
- OOA 2-folding [i] based on OA(32⁵⁰, 8388602, S₃₂, 11), using
  - discarding factors based on OA(32⁵⁰, large, S₃₂, 11), using
    - discarding parts of the base [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive.

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

None.