MinT - Information on Result #661767

Information on Result #661767

Linear OA(16⁸⁶, 90, F₁₆, 77) (dual of [90, 4, 78]-code), using juxtaposition based on

linear OA(16¹⁹, 23, F₁₆, 18) (dual of [23, 4, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹⁹, 24, F₁₆, 18) (dual of [24, 5, 19]-code), using
  - extended algebraic-geometric code AG_e(F,5P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]
linear OA(16⁶³, 67, F₁₆, 58) (dual of [67, 4, 59]-code), using
- constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,8P) [i] based on
  1. linear OA(16⁶¹, 64, F₁₆, 58) (dual of [64, 3, 59]-code), using algebraic-geometric code AG(F,5P) 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(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 (see above)
  3. linear OA(16², 3, F₁₆, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,16)), using
    - dual of repetition code with length 3 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(16⁸⁶, 45, F₁₆, 2, 77) (dual of [(45, 2), 4, 78]-NRT-code)	[i]		OOA Folding