MinT - Information on Result #2529020

Information on Result #2529020

Linear OOA(2²²², 125, F₂, 2, 106) (dual of [(125, 2), 28, 107]-NRT-code), using strength reduction based on linear OOA(2²²², 125, F₂, 2, 107) (dual of [(125, 2), 28, 108]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. 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]
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: 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(2²²⁴, 126, F₂, 2, 106) (dual of [(126, 2), 28, 107]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²²⁶, 127, F₂, 2, 106) (dual of [(127, 2), 28, 107]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²²³, 125, F₂, 2, 106) (dual of [(125, 2), 27, 107]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²²¹, 124, F₂, 2, 105) (dual of [(124, 2), 27, 106]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(2²²⁰, 124, F₂, 2, 104) (dual of [(124, 2), 28, 105]-NRT-code)	[i]
6	Linear OOA(2²¹⁹, 123, F₂, 2, 103) (dual of [(123, 2), 27, 104]-NRT-code)	[i]
7	Linear OOA(2²¹⁸, 123, F₂, 2, 102) (dual of [(123, 2), 28, 103]-NRT-code)	[i]