MinT - Information on Result #902763

Information on Result #902763

Linear OOA(32¹⁰⁵, 637, F₃₂, 2, 38) (dual of [(637, 2), 1169, 39]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32³⁰, 120, F₃₂, 2, 19) (dual of [(120, 2), 210, 20]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,220P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
  - a function field by SÃ©mirat [i]
linear OOA(32⁷⁵, 517, F₃₂, 2, 38) (dual of [(517, 2), 959, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁷⁵, 1034, F₃₂, 38) (dual of [1034, 959, 39]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁷⁵, 1035, F₃₂, 38) (dual of [1035, 960, 39]-code), using
    - constructionÂ X applied to C_e(37) âŠ‚ C_e(33) [i] based on
      1. linear OA(32⁷², 1024, F₃₂, 38) (dual of [1024, 952, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
      2. linear OA(32⁶⁴, 1024, F₃₂, 34) (dual of [1024, 960, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      3. linear OA(32³, 11, F₃₂, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
        discarding factors / shortening the dual code based on linear OA(32³, 32, F₃₂, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
        Reedâ€“Solomon code RS(29,32) [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.