MinT - Information on Result #2490460

Information on Result #2490460

Linear OOA(3²¹⁴, 209, F₃, 2, 66) (dual of [(209, 2), 204, 67]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²¹², 208, F₃, 2, 66) (dual of [(208, 2), 204, 67]-NRT-code), using

strength reduction [i] based on linear OOA(3²¹², 208, F₃, 2, 67) (dual of [(208, 2), 204, 68]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(27³⁶, 52, F₂₇, 2, 33) (dual of [(52, 2), 68, 34]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,70P) [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²¹⁵, 209, F₃, 2, 66) (dual of [(209, 2), 203, 67]-NRT-code)	[i]		OOA Duplication