MinT - Information on Result #2613318

Information on Result #2613318

Linear OOA(2¹⁵², 66, F₂, 3, 68) (dual of [(66, 3), 46, 69]-NRT-code), using strength reduction based on linear OOA(2¹⁵², 66, F₂, 3, 69) (dual of [(66, 3), 46, 70]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁴³, 22, F₄, 3, 34) (dual of [(22, 3), 23, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,31P) [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
    - an explicitly constructive algebraic function field [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(2¹⁵⁵, 67, F₂, 3, 68) (dual of [(67, 3), 46, 69]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁵², 33, F₂, 6, 68) (dual of [(33, 6), 46, 69]-NRT-code)	[i]		OOA Folding