MinT - Information on Result #901989

Information on Result #901989

Linear OOA(32⁵⁰, 16451, F₃₂, 2, 14) (dual of [(16451, 2), 32852, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁰, 66, F₃₂, 2, 7) (dual of [(66, 2), 122, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32³, 33, F₃₂, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;63,32) [i]
  2. linear OOA(32⁷, 33, F₃₂, 2, 7) (dual of [(33, 2), 59, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;59,32) [i]
linear OOA(32⁴⁰, 16385, F₃₂, 2, 14) (dual of [(16385, 2), 32730, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁴⁰, 32770, F₃₂, 14) (dual of [32770, 32730, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁴⁰, 32771, F₃₂, 14) (dual of [32771, 32731, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. linear OA(32⁴⁰, 32768, F₃₂, 14) (dual of [32768, 32728, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(32³⁷, 32768, F₃₂, 13) (dual of [32768, 32731, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(32⁰, 3, F₃₂, 0) (dual of [3, 3, 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]

Mode: Constructive and 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.