MinT - Information on Result #1298761

Information on Result #1298761

Linear OA(3¹⁵⁹, 185, F₃, 77) (dual of [185, 26, 78]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁵⁶, 180, F₃, 77) (dual of [180, 24, 78]-code), using
- concatenation of two codes [i] based on
  1. linear OA(27¹², 20, F₂₇, 12) (dual of [20, 8, 13]-code or 20-arc in PG(11,27)), using
    - discarding factors / shortening the dual code based on linear OA(27¹², 27, F₂₇, 12) (dual of [27, 15, 13]-code or 27-arc in PG(11,27)), using
      - Reedâ€“Solomon code RS(15,27) [i]
  2. linear OA(3⁶, 9, F₃, 5) (dual of [9, 3, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁶, 10, F₃, 5) (dual of [10, 4, 6]-code), using
      - projective code from ovoid in PG(3,Â 3) [i]
linear OA(3¹⁵⁶, 182, F₃, 75) (dual of [182, 26, 76]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁵⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 256 015770 691635 852283 934166 628652 916549 843567 477760 574778 388465 337037 050931 [i]
linear OA(3¹, 3, F₃, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁶⁰, 187, F₃, 77) (dual of [187, 27, 78]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound