MinT - Information on Result #2424745

Information on Result #2424745

Linear OOA(2²⁰⁶, 115, F₂, 2, 100) (dual of [(115, 2), 24, 101]-NRT-code), using strength reduction based on linear OOA(2²⁰⁶, 115, F₂, 2, 101) (dual of [(115, 2), 24, 102]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁷, 23, F₁₆, 16) (dual of [23, 6, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁷, 24, F₁₆, 16) (dual of [24, 7, 17]-code), using
    - extended algebraic-geometric code AG_e(F,7P) [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(2²⁰⁸, 116, F₂, 2, 100) (dual of [(116, 2), 24, 101]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁰⁷, 115, F₂, 2, 100) (dual of [(115, 2), 23, 101]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁵, 114, F₂, 2, 99) (dual of [(114, 2), 23, 100]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁰⁴, 114, F₂, 2, 98) (dual of [(114, 2), 24, 99]-NRT-code)	[i]
5	Linear OOA(2²⁰³, 113, F₂, 2, 97) (dual of [(113, 2), 23, 98]-NRT-code)	[i]
6	Linear OOA(2²⁰², 113, F₂, 2, 96) (dual of [(113, 2), 24, 97]-NRT-code)	[i]
7	Linear OOA(2²⁰¹, 112, F₂, 2, 95) (dual of [(112, 2), 23, 96]-NRT-code)	[i]
8	Linear OOA(2²⁰⁰, 112, F₂, 2, 94) (dual of [(112, 2), 24, 95]-NRT-code)	[i]
9	Linear OOA(2¹⁹⁹, 111, F₂, 2, 93) (dual of [(111, 2), 23, 94]-NRT-code)	[i]
10	Linear OOA(2¹⁹⁸, 111, F₂, 2, 92) (dual of [(111, 2), 24, 93]-NRT-code)	[i]
11	Linear OOA(2¹⁹⁷, 110, F₂, 2, 91) (dual of [(110, 2), 23, 92]-NRT-code)	[i]