MinT - Information on Result #902298

Information on Result #902298

Linear OOA(32⁹⁷, 524367, F₃₂, 2, 21) (dual of [(524367, 2), 1048637, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁶, 77, F₃₂, 2, 10) (dual of [(77, 2), 138, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32⁵, 33, F₃₂, 2, 5) (dual of [(33, 2), 61, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;61,32) [i]
  2. linear OOA(32¹¹, 44, F₃₂, 2, 10) (dual of [(44, 2), 77, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,77P) [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(32⁸¹, 524290, F₃₂, 2, 21) (dual of [(524290, 2), 1048499, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁸¹, 1048580, F₃₂, 21) (dual of [1048580, 1048499, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
    1. linear OA(32⁸¹, 1048576, F₃₂, 21) (dual of [1048576, 1048495, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. linear OA(32⁷⁷, 1048576, F₃₂, 20) (dual of [1048576, 1048499, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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.