MinT - Information on Result #664967

Information on Result #664967

Linear OA(16⁷⁷, 581, F₁₆, 28) (dual of [581, 504, 29]-code), using (u,Â u+v)-construction based on

linear OA(16²¹, 67, F₁₆, 14) (dual of [67, 46, 15]-code), using
- constructionÂ X applied to AG(F,49P) âŠ‚ AG(F,51P) [i] based on
  1. linear OA(16²⁰, 64, F₁₆, 14) (dual of [64, 44, 15]-code), using algebraic-geometric code AG(F,49P) [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(16¹⁸, 64, F₁₆, 12) (dual of [64, 46, 13]-code), using algebraic-geometric code AG(F,51P) [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(16⁵⁶, 514, F₁₆, 28) (dual of [514, 458, 29]-code), using
- trace code [i] based on linear OA(256²⁸, 257, F₂₅₆, 28) (dual of [257, 229, 29]-code or 257-arc in PG(27,256)), using
  - extended Reedâ€“Solomon code RS_e(229,256) [i]
  - algebraic-geometric code AG(F,114P) 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,76P) with 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+45P) with degQ = 3 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(16⁷⁷, 290, F₁₆, 2, 28) (dual of [(290, 2), 503, 29]-NRT-code)	[i]		OOA Folding