MinT - Information on Result #2435873

Information on Result #2435873

Linear OOA(3²¹⁴, 132, F₃, 2, 106) (dual of [(132, 2), 50, 107]-NRT-code), using strength reduction based on linear OOA(3²¹⁴, 132, F₃, 2, 107) (dual of [(132, 2), 50, 108]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁴¹, 33, F₉, 2, 35) (dual of [(33, 2), 25, 36]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁴¹, 34, F₉, 2, 35) (dual of [(34, 2), 27, 36]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,32P) [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [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(3²¹³, 131, F₃, 2, 105) (dual of [(131, 2), 49, 106]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(3²¹⁴, 66, F₃, 4, 106) (dual of [(66, 4), 50, 107]-NRT-code)	[i]		OOA Folding