MinT - Information on Result #2437808

Information on Result #2437808

Linear OOA(3²⁴³, 228, F₃, 2, 78) (dual of [(228, 2), 213, 79]-NRT-code), using strength reduction based on linear OOA(3²⁴³, 228, F₃, 2, 79) (dual of [(228, 2), 213, 80]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(27⁴³, 57, F₂₇, 2, 39) (dual of [(57, 2), 71, 40]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27⁴³, 64, F₂₇, 2, 39) (dual of [(64, 2), 85, 40]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,88P) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁴³, 114, F₃, 4, 78) (dual of [(114, 4), 213, 79]-NRT-code)	[i]		OOA Folding