MinT - Information on Result #664767

Information on Result #664767

Linear OA(16⁸¹, 116, F₁₆, 47) (dual of [116, 35, 48]-code), using (u,Â u+v)-construction based on

linear OA(16²⁹, 58, F₁₆, 23) (dual of [58, 29, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(16²⁹, 64, F₁₆, 23) (dual of [64, 35, 24]-code), using
  - algebraic-geometric code AG(F,40P) [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(16⁵², 58, F₁₆, 47) (dual of [58, 6, 48]-code), using
- 7 times truncation [i] based on linear OA(16⁵⁹, 65, F₁₆, 54) (dual of [65, 6, 55]-code), using
  - constructionÂ X applied to AG(F,9P) âŠ‚ AG(F,10P) [i] based on
    1. 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, using the Hermitian function field over F₁₆ [i]
    2. linear OA(16⁵⁸, 64, F₁₆, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) 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(16⁸¹, 58, F₁₆, 2, 47) (dual of [(58, 2), 35, 48]-NRT-code)	[i]		OOA Folding