MinT - Information on Result #664925

Information on Result #664925

Linear OA(16⁸², 581, F₁₆, 30) (dual of [581, 499, 31]-code), using (u,Â u+v)-construction based on

linear OA(16²², 67, F₁₆, 15) (dual of [67, 45, 16]-code), using
- constructionÂ X applied to AG(F,48P) âŠ‚ AG(F,50P) [i] based on
  1. linear OA(16²¹, 64, F₁₆, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [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(16¹⁹, 64, F₁₆, 13) (dual of [64, 45, 14]-code), using algebraic-geometric code AG(F,50P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(16⁶⁰, 514, F₁₆, 30) (dual of [514, 454, 31]-code), using
- trace code [i] based on linear OA(256³⁰, 257, F₂₅₆, 30) (dual of [257, 227, 31]-code or 257-arc in PG(29,256)), using
  - extended Reedâ€“Solomon code RS_e(227,256) [i]
  - algebraic-geometric code AG(F,113P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
  - algebraic-geometric code AG(F, Q+74P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  - algebraic-geometric code AG(F, Q+44P) with degQ = 6 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)

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 OOA(16⁸², 290, F₁₆, 2, 30) (dual of [(290, 2), 498, 31]-NRT-code)	[i]		OOA Folding