MinT - Information on Result #2657061

Information on Result #2657061

Linear OOA(2¹⁹², 86, F₂, 3, 80) (dual of [(86, 3), 66, 81]-NRT-code), using 1 step truncation based on linear OOA(2¹⁹³, 87, F₂, 3, 81) (dual of [(87, 3), 68, 82]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁵³, 29, F₄, 3, 40) (dual of [(29, 3), 34, 41]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,46P) [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
    - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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(2¹⁹², 43, F₂, 5, 80) (dual of [(43, 5), 23, 81]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁹², 43, F₂, 6, 80) (dual of [(43, 6), 66, 81]-NRT-code)	[i]		OOA Folding