MinT - Information on Result #1313993

Information on Result #1313993

Linear OA(16⁸⁵, 797, F₁₆, 36) (dual of [797, 712, 37]-code), using 208 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 15 times 0, 1, 27 times 0, 1, 40 times 0, 1, 50 times 0, 1, 57 times 0) based on linear OA(16⁷⁴, 578, F₁₆, 36) (dual of [578, 504, 37]-code), using

trace code [i] based on linear OA(256³⁷, 289, F₂₅₆, 36) (dual of [289, 252, 37]-code), using
- extended algebraic-geometric code AG_e(F,252P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
  - sharp bound on the number of rational points on curves with genus 1 [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		This result only	Method
1	Linear OOA(16⁸⁵, 797, F₁₆, 2, 36) (dual of [(797, 2), 1509, 37]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (49, 85, 797)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound