MinT - Information on Result #2231231

Information on Result #2231231

Linear OA(3¹²⁸, 191, F₃, 50) (dual of [191, 63, 51]-code), using 1 times truncation based on linear OA(3¹²⁹, 192, F₃, 51) (dual of [192, 63, 52]-code), using

concatenation of two codes [i] based on
1. linear OA(27²⁷, 48, F₂₇, 25) (dual of [48, 21, 26]-code), using
  - extended algebraic-geometric code AG_e(F,22P) [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
    - a function field by GarcÃa and Quoos [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(3¹³⁰, 193, F₃, 50) (dual of [193, 63, 51]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3¹³¹, 194, F₃, 50) (dual of [194, 63, 51]-code)	[i]
3	Linear OA(3¹³², 195, F₃, 50) (dual of [195, 63, 51]-code)	[i]
4	Linear OOA(3¹²⁸, 95, F₃, 2, 50) (dual of [(95, 2), 62, 51]-NRT-code)	[i]	OOA Folding