MinT - Information on Result #1298854

Information on Result #1298854

Linear OA(3¹⁷⁰, 198, F₃, 82) (dual of [198, 28, 83]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁶⁹, 196, F₃, 82) (dual of [196, 27, 83]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(3¹⁶⁸, 194, F₃, 82) (dual of [194, 26, 83]-code), using
    - constructionÂ X with VarÅ¡amov bound [i] based on
      1. 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
        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]
        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]
      2. 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]
      3. 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]
  2. linear OA(3¹⁶⁸, 195, F₃, 81) (dual of [195, 27, 82]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁶⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 134 575298 842102 332292 957380 502759 801663 212254 220710 583366 532136 497407 371672 350473 [i]
  3. linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]
linear OA(3¹⁶⁹, 197, F₃, 81) (dual of [197, 28, 82]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁶⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 382 206621 637734 990152 623986 984922 361201 705852 803492 156856 607863 561992 880086 607697 [i]
linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code) (see above)

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁷¹, 200, F₃, 82) (dual of [200, 29, 83]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound