MinT - Information on Result #664927

Information on Result #664927

Linear OA(16⁸³, 585, F₁₆, 30) (dual of [585, 502, 31]-code), using (u,Â u+v)-construction based on

linear OA(16²¹, 65, F₁₆, 15) (dual of [65, 44, 16]-code), using
- extended algebraic-geometric code AG_e(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]
linear OA(16⁶², 520, F₁₆, 30) (dual of [520, 458, 31]-code), using
- trace code [i] based on linear OA(256³¹, 260, F₂₅₆, 30) (dual of [260, 229, 31]-code), using
  - constructionÂ X applied to AG(F,113P) âŠ‚ AG(F,114P) [i] based on
    1. linear OA(256³⁰, 257, F₂₅₆, 30) (dual of [257, 227, 31]-code or 257-arc in PG(29,256)), using 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]
    2. linear OA(256²⁸, 257, F₂₅₆, 28) (dual of [257, 229, 29]-code or 257-arc in PG(27,256)), using 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 (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 and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(16⁸³, 292, F₁₆, 2, 30) (dual of [(292, 2), 501, 31]-NRT-code)	[i]		OOA Folding