MinT - Information on Result #2622534

Information on Result #2622534

Linear OOA(3¹³³, 57, F₃, 3, 72) (dual of [(57, 3), 38, 73]-NRT-code), using strength reduction based on linear OOA(3¹³³, 57, F₃, 3, 73) (dual of [(57, 3), 38, 74]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9³⁸, 19, F₉, 3, 36) (dual of [(19, 3), 19, 37]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9³⁸, 20, F₉, 3, 36) (dual of [(20, 3), 22, 37]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,23P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]
2. linear OA(3¹, 3, F₃, 1) (dual of [3, 2, 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(3¹³⁴, 57, F₃, 3, 72) (dual of [(57, 3), 37, 73]-NRT-code)	[i]		OOA Duplication