MinT - Information on Result #668343

Information on Result #668343

Linear OA(32⁹⁷, 1090, F₃₂, 39) (dual of [1090, 993, 40]-code), using (u,Â u+v)-construction based on

linear OA(32²³, 66, F₃₂, 19) (dual of [66, 43, 20]-code), using
- constructionÂ X applied to AG(F,43P) âŠ‚ AG(F,45P) [i] based on
  1. linear OA(32²², 63, F₃₂, 19) (dual of [63, 41, 20]-code), using algebraic-geometric code AG(F,43P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]
  2. linear OA(32²⁰, 63, F₃₂, 17) (dual of [63, 43, 18]-code), using algebraic-geometric code AG(F,45P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64 (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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