MinT - Information on Result #2254725

Information on Result #2254725

Linear OA(16⁸⁷, 104, F₁₆, 62) (dual of [104, 17, 63]-code), using 1 times truncation based on linear OA(16⁸⁸, 105, F₁₆, 63) (dual of [105, 17, 64]-code), using

constructionÂ X applied to AG(F,0P) âŠ‚ AG(F,22P) [i] based on
1. linear OA(16⁶³, 64, F₁₆, 63) (dual of [64, 1, 64]-code or 64-arc in PG(62,16)), using algebraic-geometric code AG(F,0P) [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(16⁴⁷, 64, F₁₆, 41) (dual of [64, 17, 42]-code), using algebraic-geometric code AG(F,22P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
3. linear OA(16²⁵, 41, F₁₆, 21) (dual of [41, 16, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²⁵, 45, F₁₆, 21) (dual of [45, 20, 22]-code), using
    - extended algebraic-geometric code AG_e(F,23P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [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(16⁸⁷, 52, F₁₆, 2, 62) (dual of [(52, 2), 17, 63]-NRT-code)	[i]		OOA Folding