MinT - Information on Result #902823

Information on Result #902823

Linear OOA(32¹⁰¹, 577, F₃₂, 2, 41) (dual of [(577, 2), 1053, 42]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32²³, 64, F₃₂, 2, 20) (dual of [(64, 2), 105, 21]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,107P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
  - a function field by SÃ©mirat [i]
linear OOA(32⁷⁸, 513, F₃₂, 2, 41) (dual of [(513, 2), 948, 42]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁷⁸, 1026, F₃₂, 41) (dual of [1026, 948, 42]-code), using
  - constructionÂ X applied to C_e(40) âŠ‚ C_e(39) [i] based on
    1. linear OA(32⁷⁸, 1024, F₃₂, 41) (dual of [1024, 946, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
    2. linear OA(32⁷⁶, 1024, F₃₂, 40) (dual of [1024, 948, 41]-code), using an extension C_e(39) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,39], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
    3. linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 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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