MinT - Information on Result #2611290

Information on Result #2611290

Linear OOA(2¹⁰², 42, F₂, 3, 54) (dual of [(42, 3), 24, 55]-NRT-code), using strength reduction based on linear OOA(2¹⁰², 42, F₂, 3, 55) (dual of [(42, 3), 24, 56]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4³⁰, 14, F₄, 3, 27) (dual of [(14, 3), 12, 28]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,14P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, 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(2¹⁰⁵, 43, F₂, 3, 54) (dual of [(43, 3), 24, 55]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁰³, 42, F₂, 3, 54) (dual of [(42, 3), 23, 55]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁰², 21, F₂, 6, 54) (dual of [(21, 6), 24, 55]-NRT-code)	[i]	OOA Folding