MinT - Information on Result #2431541

Information on Result #2431541

Linear OOA(3¹¹⁶, 68, F₃, 2, 67) (dual of [(68, 2), 20, 68]-NRT-code), using strength reduction based on linear OOA(3¹¹⁶, 68, F₃, 2, 68) (dual of [(68, 2), 20, 69]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9²⁴, 17, F₉, 2, 22) (dual of [(17, 2), 10, 23]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9²⁴, 20, F₉, 2, 22) (dual of [(20, 2), 16, 23]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,17P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]
2. 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: Constructive and 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹¹⁵, 67, F₃, 2, 66) (dual of [(67, 2), 19, 67]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(3¹¹⁶, 34, F₃, 4, 67) (dual of [(34, 4), 20, 68]-NRT-code)	[i]		OOA Folding