MinT - Information on Result #902803

Information on Result #902803

Linear OOA(32¹⁰⁷, 633, F₃₂, 2, 40) (dual of [(633, 2), 1159, 41]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32³¹, 120, F₃₂, 2, 20) (dual of [(120, 2), 209, 21]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,219P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
  - a function field by SÃ©mirat [i]
linear OOA(32⁷⁶, 513, F₃₂, 2, 40) (dual of [(513, 2), 950, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁷⁶, 1026, F₃₂, 40) (dual of [1026, 950, 41]-code), using
  - constructionÂ X applied to C_e(39) âŠ‚ C_e(38) [i] based on
    1. 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]
    2. linear OA(32⁷⁴, 1024, F₃₂, 39) (dual of [1024, 950, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [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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