MinT - Information on Result #2614874

Information on Result #2614874

Linear OOA(2¹⁸⁰, 84, F₂, 3, 72) (dual of [(84, 3), 72, 73]-NRT-code), using strength reduction based on linear OOA(2¹⁸⁰, 84, F₂, 3, 73) (dual of [(84, 3), 72, 74]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁴⁸, 28, F₄, 3, 36) (dual of [(28, 3), 36, 37]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,47P) [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, 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(2¹⁸¹, 84, F₂, 3, 72) (dual of [(84, 3), 71, 73]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁸⁰, 42, F₂, 5, 72) (dual of [(42, 5), 30, 73]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2¹⁸⁰, 42, F₂, 6, 72) (dual of [(42, 6), 72, 73]-NRT-code)	[i]	OOA Folding