MinT - Information on Result #661734

Information on Result #661734

Linear OA(16¹³⁰, 139, F₁₆, 106) (dual of [139, 9, 107]-code), using juxtaposition based on

linear OA(16⁵⁶, 65, F₁₆, 50) (dual of [65, 9, 51]-code), using
- extended algebraic-geometric code AG_e(F,14P) [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(16⁶⁵, 74, F₁₆, 55) (dual of [74, 9, 56]-code), using
- constructionÂ X applied to AG(F,8P) âŠ‚ AG(F,14P) [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(16⁵⁵, 64, F₁₆, 49) (dual of [64, 9, 50]-code), using algebraic-geometric code AG(F,14P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16⁵, 10, F₁₆, 5) (dual of [10, 5, 6]-code or 10-arc in PG(4,16)), using
    - discarding factors / shortening the dual code based on linear OA(16⁵, 16, F₁₆, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
      - Reedâ€“Solomon code RS(11,16) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(16¹³⁰, 139, F₁₆, 105) (dual of [139, 9, 106]-code)	[i]		Strength Reduction