MinT - Information on Result #668307

Information on Result #668307

Linear OA(32⁷², 164, F₃₂, 41) (dual of [164, 92, 42]-code), using (u,Â u+v)-construction based on

linear OA(32²⁴, 66, F₃₂, 20) (dual of [66, 42, 21]-code), using
- constructionÂ X applied to AG(F,42P) âŠ‚ AG(F,44P) [i] based on
  1. linear OA(32²³, 63, F₃₂, 20) (dual of [63, 40, 21]-code), using algebraic-geometric code AG(F,42P) [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(32²¹, 63, F₃₂, 18) (dual of [63, 42, 19]-code), using algebraic-geometric code AG(F,44P) [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(32⁴⁸, 98, F₃₂, 41) (dual of [98, 50, 42]-code), using
- extended algebraic-geometric code AG_e(F,56P) [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
  - a function field by SÃ©mirat [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(32⁷², 82, F₃₂, 2, 41) (dual of [(82, 2), 92, 42]-NRT-code)	[i]		OOA Folding