MinT - Information on Result #906869

Information on Result #906869

Linear OOA(32⁶⁹, 524389, F₃₂, 2, 15) (dual of [(524389, 2), 1048709, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹², 99, F₃₂, 2, 7) (dual of [(99, 2), 186, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(32², 33, F₃₂, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;64,32) [i]
  2. 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]
  3. 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(32⁵⁷, 524290, F₃₂, 2, 15) (dual of [(524290, 2), 1048523, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁵⁷, 1048580, F₃₂, 15) (dual of [1048580, 1048523, 16]-code), using
  - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
    1. linear OA(32⁵⁷, 1048576, F₃₂, 15) (dual of [1048576, 1048519, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    2. linear OA(32⁵³, 1048576, F₃₂, 14) (dual of [1048576, 1048523, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.