MinT - Information on Result #671644

Information on Result #671644

Linear OA(256⁵⁹, 520, F₂₅₆, 38) (dual of [520, 461, 39]-code), using (u,Â u+v)-construction based on

linear OA(256²⁰, 260, F₂₅₆, 19) (dual of [260, 240, 20]-code), using
- constructionÂ X applied to AG(F, Q+117P) âŠ‚ AG(F, Q+118P) [i] based on
  1. linear OA(256¹⁹, 257, F₂₅₆, 19) (dual of [257, 238, 20]-code or 257-arc in PG(18,256)), using algebraic-geometric code AG(F, Q+117P) with degQ = 3 and 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]
  2. linear OA(256¹⁷, 257, F₂₅₆, 17) (dual of [257, 240, 18]-code or 257-arc in PG(16,256)), using algebraic-geometric code AG(F, Q+118P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(256³⁹, 260, F₂₅₆, 38) (dual of [260, 221, 39]-code), using
- constructionÂ X applied to AG(F,109P) âŠ‚ AG(F,110P) [i] based on
  1. linear OA(256³⁸, 257, F₂₅₆, 38) (dual of [257, 219, 39]-code or 257-arc in PG(37,256)), using algebraic-geometric code AG(F,109P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  2. linear OA(256³⁶, 257, F₂₅₆, 36) (dual of [257, 221, 37]-code or 257-arc in PG(35,256)), using algebraic-geometric code AG(F,110P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code) (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	OA(128⁶⁸, 520, S₁₂₈, 38)	[i]		Discarding Parts of the Base for OAs