MinT - Information on Result #1301934

Information on Result #1301934

Linear OA(5¹⁴⁸, 171, F₅, 90) (dual of [171, 23, 91]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹⁴⁷, 169, F₅, 90) (dual of [169, 22, 91]-code), using
- 1 times truncation [i] based on linear OA(5¹⁴⁸, 170, F₅, 91) (dual of [170, 22, 92]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(25²³, 34, F₂₅, 22) (dual of [34, 11, 23]-code), using
      - discarding factors / shortening the dual code based on linear OA(25²³, 36, F₂₅, 22) (dual of [36, 13, 23]-code), using
        extended algebraic-geometric code AG_e(F,13P) [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]
linear OA(5¹⁴⁷, 170, F₅, 89) (dual of [170, 23, 90]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹⁴⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 5 181348 219278 079528 828931 583164 308735 368556 699280 852855 678905 347933 185079 723224 001722 035400 593499 898085 [i]
linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(5¹⁴⁹, 173, F₅, 90) (dual of [173, 24, 91]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound