MinT - Information on Result #1466855

Information on Result #1466855

Linear OOA(2²²², 125, F₂, 2, 107) (dual of [(125, 2), 28, 108]-NRT-code), using concatenation of two NRT-codes based on

linear OA(16¹⁸, 25, F₁₆, 17) (dual of [25, 7, 18]-code), using
- extended algebraic-geometric code AG_e(F,7P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 25, using
  - sharp bound on the number of rational points on curves with genus 1 [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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²²², 125, F₂, 2, 106) (dual of [(125, 2), 28, 107]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²²², 125, F₂, 2, 105) (dual of [(125, 2), 28, 106]-NRT-code)	[i]
3	Linear OOA(2²²², 125, F₂, 2, 104) (dual of [(125, 2), 28, 105]-NRT-code)	[i]
4	Linear OOA(2²²², 125, F₂, 2, 103) (dual of [(125, 2), 28, 104]-NRT-code)	[i]
5	Linear OOA(2²²⁴, 126, F₂, 2, 107) (dual of [(126, 2), 28, 108]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
6	Linear OOA(2²²⁶, 127, F₂, 2, 107) (dual of [(127, 2), 28, 108]-NRT-code)	[i]
7	Linear OOA(2²²⁸, 128, F₂, 2, 107) (dual of [(128, 2), 28, 108]-NRT-code)	[i]
8	Linear OOA(2²²³, 125, F₂, 2, 107) (dual of [(125, 2), 27, 108]-NRT-code)	[i]	OOA Duplication
9	Linear OOA(2²²¹, 124, F₂, 2, 106) (dual of [(124, 2), 27, 107]-NRT-code)	[i]	Truncation for OOAs
10	Linear OOA(2²²⁰, 124, F₂, 2, 105) (dual of [(124, 2), 28, 106]-NRT-code)	[i]
11	Linear OOA(2²¹⁹, 123, F₂, 2, 104) (dual of [(123, 2), 27, 105]-NRT-code)	[i]
12	Linear OOA(2²¹⁸, 123, F₂, 2, 103) (dual of [(123, 2), 28, 104]-NRT-code)	[i]
13	Linear OOA(2²¹⁷, 122, F₂, 2, 102) (dual of [(122, 2), 27, 103]-NRT-code)	[i]