MinT - Information on Result #667897

Information on Result #667897

Linear OA(32¹⁰⁹, 1114, F₃₂, 39) (dual of [1114, 1005, 40]-code), using (u,Â uâˆ’v,Â u+v+w)-construction based on

linear OA(32¹⁴, 44, F₃₂, 13) (dual of [44, 30, 14]-code), using
- extended algebraic-geometric code AG_e(F,30P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
  - a function field by SÃ©mirat [i]
linear OA(32²¹, 46, F₃₂, 19) (dual of [46, 25, 20]-code), using
- constructionÂ X applied to AG(F,23P) âŠ‚ AG(F,25P) [i] based on
  1. linear OA(32²⁰, 43, F₃₂, 19) (dual of [43, 23, 20]-code), using algebraic-geometric code AG(F,23P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44 (see above)
  2. linear OA(32¹⁸, 43, F₃₂, 17) (dual of [43, 25, 18]-code), using algebraic-geometric code AG(F,25P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44 (see above)
  3. linear OA(32¹, 3, F₃₂, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
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]

Mode: Constructive and linear.

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