MinT - Information on Result #664763

Information on Result #664763

Linear OA(16⁹³, 130, F₁₆, 55) (dual of [130, 37, 56]-code), using (u,Â u+v)-construction based on

linear OA(16³³, 65, F₁₆, 27) (dual of [65, 32, 28]-code), using
- extended algebraic-geometric code AG_e(F,37P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]
linear OA(16⁶⁰, 65, F₁₆, 55) (dual of [65, 5, 56]-code), using
- constructionÂ X applied to AG(F,8P) âŠ‚ AG(F,9P) [i] based on
  1. linear OA(16⁶⁰, 64, F₁₆, 55) (dual of [64, 4, 56]-code), using algebraic-geometric code AG(F,8P) with known gap numbers [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using the Hermitian function field over F₁₆ [i]
  2. linear OA(16⁵⁹, 64, F₁₆, 54) (dual of [64, 5, 55]-code), using algebraic-geometric code AG(F,9P) with known gap numbers [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(16⁹³, 65, F₁₆, 2, 55) (dual of [(65, 2), 37, 56]-NRT-code)	[i]		OOA Folding