MinT - Information on Result #668104

Information on Result #668104

Linear OA(32⁸⁸, 32859, F₃₂, 23) (dual of [32859, 32771, 24]-code), using (u,Â uâˆ’v,Â u+v+w)-construction based on

linear OA(32⁸, 44, F₃₂, 7) (dual of [44, 36, 8]-code), using
- extended algebraic-geometric code AG_e(F,36P) [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(32¹³, 46, F₃₂, 11) (dual of [46, 33, 12]-code), using
- constructionÂ X applied to AG(F,31P) âŠ‚ AG(F,33P) [i] based on
  1. linear OA(32¹², 43, F₃₂, 11) (dual of [43, 31, 12]-code), using algebraic-geometric code AG(F,31P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44 (see above)
  2. linear OA(32¹⁰, 43, F₃₂, 9) (dual of [43, 33, 10]-code), using algebraic-geometric code AG(F,33P) [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(32⁶⁷, 32769, F₃₂, 23) (dual of [32769, 32702, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]

Mode: Constructive and linear.

None.

None.