MinT - Information on Result #2226714

Information on Result #2226714

Linear OA(2²⁴², 354, F₂, 68) (dual of [354, 112, 69]-code), using 1 times truncation based on linear OA(2²⁴³, 355, F₂, 69) (dual of [355, 112, 70]-code), using

concatenation of two codes [i] based on
1. linear OA(16⁴³, 71, F₁₆, 34) (dual of [71, 28, 35]-code), using
  - constructionÂ X applied to AG(F,29P) âŠ‚ AG(F,33P) [i] based on
    1. linear OA(16⁴⁰, 64, F₁₆, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [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(16³⁶, 64, F₁₆, 30) (dual of [64, 28, 31]-code), using algebraic-geometric code AG(F,33P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    3. linear OA(16³, 7, F₁₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
      - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
        Reedâ€“Solomon code RS(13,16) [i]
2. 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.

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(2²⁴², 177, F₂, 2, 68) (dual of [(177, 2), 112, 69]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴², 118, F₂, 3, 68) (dual of [(118, 3), 112, 69]-NRT-code)	[i]		OOA Folding