MinT - Information on Result #2235005

Information on Result #2235005

Linear OA(3²²⁷, 499, F₃, 62) (dual of [499, 272, 63]-code), using 1 times truncation based on linear OA(3²²⁸, 500, F₃, 63) (dual of [500, 272, 64]-code), using

concatenation of two codes [i] based on
1. linear OA(81³², 100, F₈₁, 31) (dual of [100, 68, 32]-code), using
  - extended algebraic-geometric code AG_e(F,68P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]
2. linear OA(3¹, 5, F₃, 1) (dual of [5, 4, 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		Method
1	Linear OA(3²²⁹, 501, F₃, 62) (dual of [501, 272, 63]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3²³⁰, 502, F₃, 62) (dual of [502, 272, 63]-code)	[i]
3	Linear OA(3²³¹, 503, F₃, 62) (dual of [503, 272, 63]-code)	[i]
4	Linear OA(3²³², 504, F₃, 62) (dual of [504, 272, 63]-code)	[i]
5	Linear OOA(3²²⁷, 249, F₃, 2, 62) (dual of [(249, 2), 271, 63]-NRT-code)	[i]	OOA Folding
6	Linear OOA(3²²⁷, 166, F₃, 3, 62) (dual of [(166, 3), 271, 63]-NRT-code)	[i]	OOA Folding