MinT - Information on Result #912022

Information on Result #912022

Linear OOA(2²⁶⁰, 140, F₂, 2, 131) (dual of [(140, 2), 20, 132]-NRT-code), using concatenation of two NRT-codes based on

linear OA(16²³, 28, F₁₆, 21) (dual of [28, 5, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(16²³, 33, F₁₆, 21) (dual of [33, 10, 22]-code), using
  - extended algebraic-geometric code AG_e(F,11P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]
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		This result only	Method
1	Linear OOA(2²⁶⁰, 140, F₂, 2, 130) (dual of [(140, 2), 20, 131]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁶⁰, 140, F₂, 2, 129) (dual of [(140, 2), 20, 130]-NRT-code)	[i]
3	Linear OOA(2²⁶⁰, 140, F₂, 2, 128) (dual of [(140, 2), 20, 129]-NRT-code)	[i]
4	Linear OOA(2²⁶⁰, 140, F₂, 2, 127) (dual of [(140, 2), 20, 128]-NRT-code)	[i]
5	Linear OOA(2²⁶⁰, 140, F₂, 2, 126) (dual of [(140, 2), 20, 127]-NRT-code)	[i]
6	Linear OOA(2²⁵⁹, 139, F₂, 2, 130) (dual of [(139, 2), 19, 131]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(2²⁵⁸, 139, F₂, 2, 129) (dual of [(139, 2), 20, 130]-NRT-code)	[i]
8	Linear OOA(2²⁵⁷, 138, F₂, 2, 128) (dual of [(138, 2), 19, 129]-NRT-code)	[i]
9	Linear OOA(2²⁵⁶, 138, F₂, 2, 127) (dual of [(138, 2), 20, 128]-NRT-code)	[i]
10	Linear OOA(2²⁶⁰, 70, F₂, 4, 131) (dual of [(70, 4), 20, 132]-NRT-code)	[i]		OOA Folding