MinT - Information on Result #668579

Information on Result #668579

Linear OA(32⁹⁶, 32835, F₃₂, 27) (dual of [32835, 32739, 28]-code), using (u,Â u+v)-construction based on

linear OA(32¹⁷, 66, F₃₂, 13) (dual of [66, 49, 14]-code), using
- constructionÂ X applied to AG(F,49P) âŠ‚ AG(F,51P) [i] based on
  1. linear OA(32¹⁶, 63, F₃₂, 13) (dual of [63, 47, 14]-code), using algebraic-geometric code AG(F,49P) [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(32¹⁴, 63, F₃₂, 11) (dual of [63, 49, 12]-code), using algebraic-geometric code AG(F,51P) [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(32⁷⁹, 32769, F₃₂, 27) (dual of [32769, 32690, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]

Mode: Constructive and linear.

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