MinT - Information on Result #2425444

Information on Result #2425444

Linear OOA(2²¹⁴, 115, F₂, 2, 112) (dual of [(115, 2), 16, 113]-NRT-code), using strength reduction based on linear OOA(2²¹⁴, 115, F₂, 2, 113) (dual of [(115, 2), 16, 114]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁹, 23, F₁₆, 18) (dual of [23, 4, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁹, 24, F₁₆, 18) (dual of [24, 5, 19]-code), using
    - extended algebraic-geometric code AG_e(F,5P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [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(2²¹⁶, 116, F₂, 2, 112) (dual of [(116, 2), 16, 113]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²¹⁵, 115, F₂, 2, 112) (dual of [(115, 2), 15, 113]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²¹², 114, F₂, 2, 110) (dual of [(114, 2), 16, 111]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²¹¹, 113, F₂, 2, 109) (dual of [(113, 2), 15, 110]-NRT-code)	[i]
5	Linear OOA(2²¹⁰, 113, F₂, 2, 108) (dual of [(113, 2), 16, 109]-NRT-code)	[i]
6	Linear OOA(2²⁰⁹, 112, F₂, 2, 107) (dual of [(112, 2), 15, 108]-NRT-code)	[i]
7	Linear OOA(2²⁰⁶, 111, F₂, 2, 104) (dual of [(111, 2), 16, 105]-NRT-code)	[i]
8	Linear OOA(2²⁰⁵, 110, F₂, 2, 103) (dual of [(110, 2), 15, 104]-NRT-code)	[i]