MinT - Information on Result #2670111

Information on Result #2670111

Linear OOA(2¹¹², 52, F₂, 3, 49) (dual of [(52, 3), 44, 50]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁰⁹, 51, F₂, 3, 49) (dual of [(51, 3), 44, 50]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4²⁹, 17, F₄, 3, 24) (dual of [(17, 3), 22, 25]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,26P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, 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(2¹¹³, 52, F₂, 3, 49) (dual of [(52, 3), 43, 50]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹¹⁴, 52, F₂, 3, 49) (dual of [(52, 3), 42, 50]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹¹², 26, F₂, 5, 49) (dual of [(26, 5), 18, 50]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2¹¹², 26, F₂, 6, 49) (dual of [(26, 6), 44, 50]-NRT-code)	[i]	OOA Folding