MinT - Information on Result #2421045

Information on Result #2421045

Linear OOA(2¹⁵⁴, 90, F₂, 2, 68) (dual of [(90, 2), 26, 69]-NRT-code), using strength reduction based on linear OOA(2¹⁵⁴, 90, F₂, 2, 69) (dual of [(90, 2), 26, 70]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁴⁷, 30, F₄, 2, 34) (dual of [(30, 2), 13, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,25P) [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(2¹⁵⁴, 45, F₂, 4, 68) (dual of [(45, 4), 26, 69]-NRT-code)	[i]		OOA Folding