MinT - Information on Result #2424444

Information on Result #2424444

Linear OOA(2²⁰², 115, F₂, 2, 94) (dual of [(115, 2), 28, 95]-NRT-code), using strength reduction based on linear OOA(2²⁰², 115, F₂, 2, 95) (dual of [(115, 2), 28, 96]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁶, 23, F₁₆, 15) (dual of [23, 7, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁶, 24, F₁₆, 15) (dual of [24, 8, 16]-code), using
    - extended algebraic-geometric code AG_e(F,8P) [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(2²⁰⁴, 116, F₂, 2, 94) (dual of [(116, 2), 28, 95]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁰³, 115, F₂, 2, 94) (dual of [(115, 2), 27, 95]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰¹, 114, F₂, 2, 93) (dual of [(114, 2), 27, 94]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁰⁰, 114, F₂, 2, 92) (dual of [(114, 2), 28, 93]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁹, 113, F₂, 2, 91) (dual of [(113, 2), 27, 92]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁸, 113, F₂, 2, 90) (dual of [(113, 2), 28, 91]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁷, 112, F₂, 2, 89) (dual of [(112, 2), 27, 90]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁶, 112, F₂, 2, 88) (dual of [(112, 2), 28, 89]-NRT-code)	[i]
9	Linear OOA(2¹⁹⁴, 111, F₂, 2, 86) (dual of [(111, 2), 28, 87]-NRT-code)	[i]
10	Linear OOA(2¹⁹³, 110, F₂, 2, 85) (dual of [(110, 2), 27, 86]-NRT-code)	[i]