MinT - Information on Result #2298651

Information on Result #2298651

Linear OA(2¹⁶⁷, 199, F₂, 66) (dual of [199, 32, 67]-code), using 1 times truncation based on linear OA(2¹⁶⁸, 200, F₂, 67) (dual of [200, 32, 68]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹⁷, 25, F₁₆, 16) (dual of [25, 8, 17]-code), using
  - extended algebraic-geometric code AG_e(F,8P) [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 OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
  - Reedâ€“Muller code RM(1,3) [i]
  - caps in base bÂ =Â 2 [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(2¹⁶⁹, 201, F₂, 66) (dual of [201, 32, 67]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(2¹⁷⁰, 202, F₂, 66) (dual of [202, 32, 67]-code)	[i]
3	Linear OA(2¹⁷¹, 203, F₂, 66) (dual of [203, 32, 67]-code)	[i]
4	Linear OA(2¹⁷², 204, F₂, 66) (dual of [204, 32, 67]-code)	[i]
5	Linear OA(2¹⁷⁷, 210, F₂, 66) (dual of [210, 33, 67]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound