MinT - Information on Result #902178

Information on Result #902178

Linear OOA(32⁸³, 524367, F₃₂, 2, 18) (dual of [(524367, 2), 1048651, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁴, 77, F₃₂, 2, 9) (dual of [(77, 2), 140, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32⁴, 33, F₃₂, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;62,32) [i]
  2. linear OOA(32¹⁰, 44, F₃₂, 2, 9) (dual of [(44, 2), 78, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,78P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]
linear OOA(32⁶⁹, 524290, F₃₂, 2, 18) (dual of [(524290, 2), 1048511, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁶⁹, 1048580, F₃₂, 18) (dual of [1048580, 1048511, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
    1. linear OA(32⁶⁹, 1048576, F₃₂, 18) (dual of [1048576, 1048507, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(32⁶⁵, 1048576, F₃₂, 17) (dual of [1048576, 1048511, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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]

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.