MinT - Information on Result #2613743

Information on Result #2613743

Linear OOA(2¹⁶⁰, 66, F₂, 3, 76) (dual of [(66, 3), 38, 77]-NRT-code), using strength reduction based on linear OOA(2¹⁶⁰, 66, F₂, 3, 77) (dual of [(66, 3), 38, 78]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁴⁷, 22, F₄, 3, 38) (dual of [(22, 3), 19, 39]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,27P) [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		Method
1	Linear OOA(2¹⁶³, 67, F₂, 3, 76) (dual of [(67, 3), 38, 77]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁶¹, 66, F₂, 3, 76) (dual of [(66, 3), 37, 77]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁶⁰, 33, F₂, 6, 76) (dual of [(33, 6), 38, 77]-NRT-code)	[i]	OOA Folding