MinT - Information on Result #1821428

Information on Result #1821428

OA(128⁶⁴, 517, S₁₂₈, 37), using discarding parts of the base based on linear OA(256⁵⁶, 517, F₂₅₆, 37) (dual of [517, 461, 38]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256¹⁸, 257, F₂₅₆, 18) (dual of [257, 239, 19]-code or 257-arc in PG(17,256)), using
  - extended Reedâ€“Solomon code RS_e(239,256) [i]
  - algebraic-geometric code AG(F,119P) 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+78P) 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+47P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
2. linear OA(256³⁸, 260, F₂₅₆, 37) (dual of [260, 222, 38]-code), using
  - constructionÂ X applied to AG(F, Q+108P) âŠ‚ AG(F, Q+109P) [i] based on
    1. linear OA(256³⁷, 257, F₂₅₆, 37) (dual of [257, 220, 38]-code or 257-arc in PG(36,256)), using algebraic-geometric code AG(F, Q+108P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
    2. linear OA(256³⁵, 257, F₂₅₆, 35) (dual of [257, 222, 36]-code or 257-arc in PG(34,256)), using algebraic-geometric code AG(F, Q+109P) 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]

Mode: Constructive.

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(128⁶⁵, 518, S₁₂₈, 37)	[i]		Code Embedding in Larger Space