MinT - Information on Result #661762

Information on Result #661762

Linear OA(16¹²⁹, 134, F₁₆, 114) (dual of [134, 5, 115]-code), using juxtaposition based on

linear OA(16⁶⁰, 65, F₁₆, 55) (dual of [65, 5, 56]-code), using
- constructionÂ X applied to AG(F,8P) âŠ‚ AG(F,9P) [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(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 (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]
linear OA(16⁶⁴, 69, F₁₆, 58) (dual of [69, 5, 59]-code), using
- constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,9P) [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(16⁵⁹, 64, F₁₆, 54) (dual of [64, 5, 55]-code) (see above)
  3. linear OA(16³, 5, F₁₆, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,16) or 5-cap in PG(2,16)), using
    - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
      - Reedâ€“Solomon code RS(13,16) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(16¹²⁶, 131, F₁₆, 111) (dual of [131, 5, 112]-code)	[i]		Truncation
2	Linear OOA(16¹²⁹, 67, F₁₆, 2, 114) (dual of [(67, 2), 5, 115]-NRT-code)	[i]		OOA Folding