MinT - Information on Result #2657051

Information on Result #2657051

Linear OOA(2²¹⁸, 86, F₂, 3, 106) (dual of [(86, 3), 40, 107]-NRT-code), using 1 step truncation based on linear OOA(2²¹⁹, 87, F₂, 3, 107) (dual of [(87, 3), 42, 108]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁶⁶, 29, F₄, 3, 53) (dual of [(29, 3), 21, 54]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,33P) [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(2²¹⁸, 43, F₂, 6, 106) (dual of [(43, 6), 40, 107]-NRT-code)	[i]		OOA Folding