MinT - Information on Result #1298836

Information on Result #1298836

Linear OA(3¹⁶⁸, 194, F₃, 82) (dual of [194, 26, 83]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁶⁴, 188, F₃, 82) (dual of [188, 24, 83]-code), using
- 1 times truncation [i] based on linear OA(3¹⁶⁵, 189, F₃, 83) (dual of [189, 24, 84]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(27¹³, 21, F₂₇, 13) (dual of [21, 8, 14]-code or 21-arc in PG(12,27)), using
      - discarding factors / shortening the dual code based on linear OA(27¹³, 27, F₂₇, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,27)), using
        Reedâ€“Solomon code RS(14,27) [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(3¹⁶⁴, 190, F₃, 79) (dual of [190, 26, 80]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁶⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 1 176427 216886 691545 330355 763998 714770 949137 558925 319751 023770 445822 603353 059091 [i]
linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reedâ€“Solomon code RS_e(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁶⁹, 196, F₃, 82) (dual of [196, 27, 83]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound