MinT - Information on Result #2627624

Information on Result #2627624

Linear OOA(3²²⁶, 84, F₃, 3, 142) (dual of [(84, 3), 26, 143]-NRT-code), using strength reduction based on linear OOA(3²²⁶, 84, F₃, 3, 143) (dual of [(84, 3), 26, 144]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁵⁰, 21, F₉, 3, 47) (dual of [(21, 3), 13, 48]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁵⁰, 28, F₉, 3, 47) (dual of [(28, 3), 34, 48]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,36P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [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(3²²⁷, 84, F₃, 3, 142) (dual of [(84, 3), 25, 143]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²²⁵, 83, F₃, 3, 141) (dual of [(83, 3), 24, 142]-NRT-code)	[i]		Truncation for OOAs