MinT - Information on Result #668005

Information on Result #668005

Linear OA(32⁸³, 1115, F₃₂, 29) (dual of [1115, 1032, 30]-code), using (u,Â uâˆ’v,Â u+v+w)-construction based on

linear OA(32¹⁰, 44, F₃₂, 9) (dual of [44, 34, 10]-code), using
- extended algebraic-geometric code AG_e(F,34P) [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(32¹⁶, 46, F₃₂, 14) (dual of [46, 30, 15]-code), using
- constructionÂ X applied to AG(F,28P) âŠ‚ AG(F,30P) [i] based on
  1. linear OA(32¹⁵, 43, F₃₂, 14) (dual of [43, 28, 15]-code), using algebraic-geometric code AG(F,28P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44 (see above)
  2. linear OA(32¹³, 43, F₃₂, 12) (dual of [43, 30, 13]-code), using algebraic-geometric code AG(F,30P) [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(32⁵⁷, 1025, F₃₂, 29) (dual of [1025, 968, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025Â | 32⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]

Mode: Constructive and linear.

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