MinT - Information on Result #906847

Information on Result #906847

Linear OOA(32⁸⁹, 524389, F₃₂, 2, 19) (dual of [(524389, 2), 1048689, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁶, 99, F₃₂, 2, 9) (dual of [(99, 2), 182, 10]-NRT-code), using
- generalized (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(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]
  3. linear OOA(32⁹, 33, F₃₂, 2, 9) (dual of [(33, 2), 57, 10]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;57,32) [i]
linear OOA(32⁷³, 524290, F₃₂, 2, 19) (dual of [(524290, 2), 1048507, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁷³, 1048580, F₃₂, 19) (dual of [1048580, 1048507, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
    1. linear OA(32⁷³, 1048576, F₃₂, 19) (dual of [1048576, 1048503, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. 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]
    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.