MinT - Information on Result #2543211

Information on Result #2543211

Linear OOA(256⁵⁷, 642, F₂₅₆, 2, 35) (dual of [(642, 2), 1227, 36]-NRT-code), using 256¹ times duplication based on linear OOA(256⁵⁶, 642, F₂₅₆, 2, 35) (dual of [(642, 2), 1228, 36]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(256¹⁹, 321, F₂₅₆, 2, 17) (dual of [(321, 2), 623, 18]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,624P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]
2. linear OOA(256³⁷, 321, F₂₅₆, 2, 35) (dual of [(321, 2), 605, 36]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,606P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)

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		This result only	Method
1	Linear OOA(256⁵⁷, 642, F₂₅₆, 3, 35) (dual of [(642, 3), 1869, 36]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(256⁵⁷, 642, F₂₅₆, 4, 35) (dual of [(642, 4), 2511, 36]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound