MinT - Information on Result #661751

Information on Result #661751

Linear OA(16¹²⁹, 135, F₁₆, 112) (dual of [135, 6, 113]-code), using juxtaposition based on

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, using the Hermitian function field over F₁₆ [i]
linear OA(16⁶⁵, 71, F₁₆, 58) (dual of [71, 6, 59]-code), using
- constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,10P) [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 (see above)
  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(16⁴, 7, F₁₆, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,16)), using
    - discarding factors / shortening the dual code based on linear OA(16⁴, 16, F₁₆, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
      - Reedâ€“Solomon code RS(12,16) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(16¹²⁹, 135, F₁₆, 111) (dual of [135, 6, 112]-code)	[i]		Strength Reduction
2	Linear OA(16¹²⁹, 135, F₁₆, 110) (dual of [135, 6, 111]-code)	[i]		Strength Reduction