MinT - Information on Result #2244133

Information on Result #2244133

Linear OA(4²⁰⁹, 407, F₄, 66) (dual of [407, 198, 67]-code), using 1 times truncation based on linear OA(4²¹⁰, 408, F₄, 67) (dual of [408, 198, 68]-code), using

concatenation of two codes [i] based on
1. linear OA(64³⁶, 102, F₆₄, 33) (dual of [102, 66, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(64³⁶, 103, F₆₄, 33) (dual of [103, 67, 34]-code), using
    - algebraic-geometric code AG(F,69P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]
2. linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²⁰⁹, 203, F₄, 2, 66) (dual of [(203, 2), 197, 67]-NRT-code)	[i]		OOA Folding