MinT - Information on Result #901891

Information on Result #901891

Linear OOA(32⁴⁷, 524334, F₃₂, 2, 11) (dual of [(524334, 2), 1048621, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32⁶, 44, F₃₂, 2, 5) (dual of [(44, 2), 82, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,82P) [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(32⁴¹, 524290, F₃₂, 2, 11) (dual of [(524290, 2), 1048539, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁴¹, 1048580, F₃₂, 11) (dual of [1048580, 1048539, 12]-code), using
  - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
    1. linear OA(32⁴¹, 1048576, F₃₂, 11) (dual of [1048576, 1048535, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(32³⁷, 1048576, F₃₂, 10) (dual of [1048576, 1048539, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.

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