MinT - Information on Result #1047721

Information on Result #1047721

Linear OOA(2¹¹⁶, 76, F₂, 3, 34) (dual of [(76, 3), 112, 35]-NRT-code), using trace code based on linear OOA(4⁵⁸, 38, F₄, 3, 34) (dual of [(38, 3), 56, 35]-NRT-code), using

constructionÂ X applied to AG(3;F,61P) âŠ‚ AG(3;F,70P) [i] based on
1. linear OOA(4⁴⁹, 32, F₄, 3, 34) (dual of [(32, 3), 47, 35]-NRT-code), using algebraic-geometric NRT-code AG(3;F,61P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(4⁴⁰, 32, F₄, 3, 25) (dual of [(32, 3), 56, 26]-NRT-code), using algebraic-geometric NRT-code AG(3;F,70P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
3. linear OOA(4⁹, 6, F₄, 3, 8) (dual of [(6, 3), 9, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁹, 9, F₄, 3, 8) (dual of [(9, 3), 18, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
      - the Hermitian function field over F₄ [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(2¹¹⁶, 38, F₂, 6, 34) (dual of [(38, 6), 112, 35]-NRT-code)	[i]		OOA Folding