MinT - Information on Result #2237137

Information on Result #2237137

Linear OA(4⁸¹, 113, F₄, 38) (dual of [113, 32, 39]-code), using 1 times truncation based on linear OA(4⁸², 114, F₄, 39) (dual of [114, 32, 40]-code), using

concatenation of two codes [i] based on
1. linear OA(16²², 38, F₁₆, 19) (dual of [38, 16, 20]-code), using
  - extended algebraic-geometric code AG_e(F,18P) [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]
2. linear OA(4¹, 3, F₄, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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		This result only	Method
1	Linear OOA(4⁸¹, 56, F₄, 2, 38) (dual of [(56, 2), 31, 39]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4⁸¹, 37, F₄, 3, 38) (dual of [(37, 3), 30, 39]-NRT-code)	[i]		OOA Folding