MinT - Information on Result #2527367

Information on Result #2527367

OOA(32⁹⁸, 4196351, S₃₂, 2, 17), using 1 times NRT-code embedding in larger space based on OOA(32⁹⁶, 4196350, S₃₂, 2, 17), using

(u,Â u+v)-construction [i] based on
1. OOA(32¹⁸, 2049, S₃₂, 2, 8), using
  - OOA 2-folding [i] based on OA(32¹⁸, 4098, S₃₂, 8), using
    - discarding parts of the base [i] based on linear OA(64¹⁵, 4098, F₆₄, 8) (dual of [4098, 4083, 9]-code), using
      - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
        linear OA(64¹⁵, 4096, F₆₄, 8) (dual of [4096, 4081, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(64¹³, 4096, F₆₄, 7) (dual of [4096, 4083, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
2. OOA(32⁷⁸, 4194301, S₃₂, 2, 17), using
  - OOA 2-folding [i] based on OA(32⁷⁸, 8388602, S₃₂, 17), using
    - discarding factors based on OA(32⁷⁸, large, S₃₂, 17), using
      - discarding parts of the base [i] based on linear OA(64⁶⁵, large, F₆₄, 17) (dual of [large, large−65, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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.