MinT - Information on Result #661459

Information on Result #661459

Linear OA(2²¹⁷, 345, F₂, 59) (dual of [345, 128, 60]-code), using concatenation of two codes based on

linear OA(16³⁷, 69, F₁₆, 29) (dual of [69, 32, 30]-code), using
- constructionÂ X applied to AG(F,34P) âŠ‚ AG(F,37P) [i] based on
  1. linear OA(16³⁵, 64, F₁₆, 29) (dual of [64, 29, 30]-code), using algebraic-geometric code AG(F,34P) [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(16³², 64, F₁₆, 26) (dual of [64, 32, 27]-code), using algebraic-geometric code AG(F,37P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16², 5, F₁₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
    - discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
      - Reedâ€“Solomon code RS(14,16) [i]
linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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: