MinT - Information on Result #661726

Information on Result #661726

Linear OA(16¹³⁰, 140, F₁₆, 104) (dual of [140, 10, 105]-code), using juxtaposition based on

linear OA(16⁵⁴, 64, F₁₆, 48) (dual of [64, 10, 49]-code), using
- algebraic-geometric code AG(F,15P) [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(16⁶⁶, 76, F₁₆, 55) (dual of [76, 10, 56]-code), using
- constructionÂ X applied to AG(F,8P) âŠ‚ AG(F,15P) [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(16⁵⁴, 64, F₁₆, 48) (dual of [64, 10, 49]-code), using algebraic-geometric code AG(F,15P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16⁶, 12, F₁₆, 6) (dual of [12, 6, 7]-code or 12-arc in PG(5,16)), using
    - discarding factors / shortening the dual code based on linear OA(16⁶, 16, F₁₆, 6) (dual of [16, 10, 7]-code or 16-arc in PG(5,16)), using
      - Reedâ€“Solomon code RS(10,16) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(16¹³⁰, 70, F₁₆, 2, 104) (dual of [(70, 2), 10, 105]-NRT-code)	[i]		OOA Folding