MinT - Information on Result #2236585

Information on Result #2236585

Linear OA(4⁸⁹, 103, F₄, 53) (dual of [103, 14, 54]-code), using 2 times truncation based on linear OA(4⁹¹, 105, F₄, 55) (dual of [105, 14, 56]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹⁴, 21, F₁₆, 13) (dual of [21, 7, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁴, 24, F₁₆, 13) (dual of [24, 10, 14]-code), using
    - extended algebraic-geometric code AG_e(F,10P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
  - extended Reedâ€“Solomon code RS_e(2,4) [i]
  - Simplex code S(2,4) [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(4⁸⁹, 51, F₄, 2, 53) (dual of [(51, 2), 13, 54]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4⁸⁹, 34, F₄, 3, 53) (dual of [(34, 3), 13, 54]-NRT-code)	[i]		OOA Folding