MinT - Information on Result #1298798

Information on Result #1298798

Linear OA(3¹⁶¹, 189, F₃, 77) (dual of [189, 28, 78]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁶⁰, 187, F₃, 77) (dual of [187, 27, 78]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(3¹⁵⁹, 185, F₃, 77) (dual of [185, 26, 78]-code), using
    - constructionÂ X with VarÅ¡amov bound [i] based on
      1. linear OA(3¹⁵⁶, 180, F₃, 77) (dual of [180, 24, 78]-code), using
        concatenation of two codes [i] based on
        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]
        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(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]
      3. 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]
  2. linear OA(3¹⁵⁹, 186, F₃, 76) (dual of [186, 27, 77]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁵⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 5936 369239 982614 546715 037052 973876 329740 376403 782383 402170 367485 120972 563491 [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(3¹⁶⁰, 188, F₃, 76) (dual of [188, 28, 77]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁶⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 16465 217057 402977 523356 196205 575499 717831 058480 330826 421827 857601 521956 209979 [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(3¹⁶², 191, F₃, 77) (dual of [191, 29, 78]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound