MinT - Information on Result #1832086

Information on Result #1832086

OOA(32⁸⁹, 4718591, S₃₂, 2, 14), using (u,Â u+v)-construction based on

linear OOA(32²⁵, 524290, F₃₂, 2, 7) (dual of [(524290, 2), 1048555, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32²⁵, 1048580, F₃₂, 7) (dual of [1048580, 1048555, 8]-code), using
  - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
    1. linear OA(32²⁵, 1048576, F₃₂, 7) (dual of [1048576, 1048551, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(32²¹, 1048576, F₃₂, 6) (dual of [1048576, 1048555, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(32⁶⁴, 4194301, S₃₂, 2, 14), using
- OOA 2-folding [i] based on OA(32⁶⁴, 8388602, S₃₂, 14), using
  - discarding factors based on OA(32⁶⁴, large, S₃₂, 14), using
    - discarding parts of the base [i] based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.