MinT - Information on Result #2462497

Information on Result #2462497

Linear OOA(3⁵⁷, 41, F₃, 2, 28) (dual of [(41, 2), 25, 29]-NRT-code), using 1 step truncation based on linear OOA(3⁵⁸, 42, F₃, 2, 29) (dual of [(42, 2), 26, 30]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9¹⁵, 14, F₉, 2, 14) (dual of [(14, 2), 13, 15]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9¹⁵, 16, F₉, 2, 14) (dual of [(16, 2), 17, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,17P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, 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(3⁵⁷, 20, F₃, 4, 28) (dual of [(20, 4), 23, 29]-NRT-code)	[i]		OOA Folding