MinT - Information on Result #2299058

Information on Result #2299058

Linear OA(2¹⁷², 317, F₂, 44) (dual of [317, 145, 45]-code), using 1 times truncation based on linear OA(2¹⁷³, 318, F₂, 45) (dual of [318, 145, 46]-code), using

concatenation of two codes [i] based on
1. linear OA(32²⁴, 53, F₃₂, 22) (dual of [53, 29, 23]-code), using
  - extended algebraic-geometric code AG_e(F,30P) [i] based on function field F/F₃₂ with g(F) = 2 and N(F) ≥ 53, using
    - sharp bound on the number of rational points on curves with genus 2 [i]
2. linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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 OA(2¹⁷⁴, 319, F₂, 44) (dual of [319, 145, 45]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(2¹⁷⁵, 321, F₂, 44) (dual of [321, 146, 45]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound