MinT - Information on Result #659105

Information on Result #659105

Linear OA(4⁷⁴, 142, F₄, 28) (dual of [142, 68, 29]-code), using trace code based on linear OA(16³⁷, 71, F₁₆, 28) (dual of [71, 34, 29]-code), using

constructionÂ X applied to AG(F,35P) âŠ‚ AG(F,39P) [i] based on
1. linear OA(16³⁴, 64, F₁₆, 28) (dual of [64, 30, 29]-code), using algebraic-geometric code AG(F,35P) [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(16³⁰, 64, F₁₆, 24) (dual of [64, 34, 25]-code), using algebraic-geometric code AG(F,39P) [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]

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(4⁷⁵, 143, F₄, 28) (dual of [143, 68, 29]-code)	[i]		Code Embedding in Larger Space
2	Linear OOA(4⁷⁴, 71, F₄, 2, 28) (dual of [(71, 2), 68, 29]-NRT-code)	[i]		OOA Folding