MinT - Information on Result #2427967

Information on Result #2427967

Linear OOA(2²⁴², 225, F₂, 2, 68) (dual of [(225, 2), 208, 69]-NRT-code), using strength reduction based on linear OOA(2²⁴², 225, F₂, 2, 69) (dual of [(225, 2), 208, 70]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16³⁸, 45, F₁₆, 2, 34) (dual of [(45, 2), 52, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,55P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 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		Method
1	Linear OOA(2²⁴⁴, 226, F₂, 2, 68) (dual of [(226, 2), 208, 69]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁴⁶, 227, F₂, 2, 68) (dual of [(227, 2), 208, 69]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²⁴³, 225, F₂, 2, 68) (dual of [(225, 2), 207, 69]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁴², 75, F₂, 5, 68) (dual of [(75, 5), 133, 69]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2²⁴², 75, F₂, 6, 68) (dual of [(75, 6), 208, 69]-NRT-code)	[i]	OOA Folding