MinT - Information on Result #2304179

Information on Result #2304179

Linear OA(5¹³⁸, 158, F₅, 85) (dual of [158, 20, 86]-code), using 2 times truncation based on linear OA(5¹⁴⁰, 160, F₅, 87) (dual of [160, 20, 88]-code), using

concatenation of two codes [i] based on
1. linear OA(25²², 32, F₂₅, 21) (dual of [32, 10, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(25²², 36, F₂₅, 21) (dual of [36, 14, 22]-code), using
    - extended algebraic-geometric code AG_e(F,14P) [i] based on function field F/F₂₅ with g(F) = 1 and N(F) ≥ 36, using
      - sharp bound on the number of rational points on curves with genus 1 [i]
2. linear OA(5³, 5, F₅, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,5) or 5-cap in PG(2,5)), using
  - Reedâ€“Solomon code RS(2,5) [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(5¹³⁹, 160, F₅, 85) (dual of [160, 21, 86]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound