MinT - Information on Result #2232768

Information on Result #2232768

Linear OA(3¹⁶⁵, 219, F₃, 66) (dual of [219, 54, 67]-code), using 1 times truncation based on linear OA(3¹⁶⁶, 220, F₃, 67) (dual of [220, 54, 68]-code), using

concatenation of two codes [i] based on
1. linear OA(27³⁷, 55, F₂₇, 33) (dual of [55, 18, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(27³⁷, 64, F₂₇, 33) (dual of [64, 27, 34]-code), using
    - extended algebraic-geometric code AG_e(F,30P) [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. linear OA(3¹, 4, F₃, 1) (dual of [4, 3, 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]

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.

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 OOA(3¹⁶⁵, 109, F₃, 2, 66) (dual of [(109, 2), 53, 67]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁶⁵, 73, F₃, 3, 66) (dual of [(73, 3), 54, 67]-NRT-code)	[i]		OOA Folding