MinT - Information on Result #2237212

Information on Result #2237212

Linear OA(4¹²⁸, 138, F₄, 84) (dual of [138, 10, 85]-code), using 7 times truncation based on linear OA(4¹³⁵, 145, F₄, 91) (dual of [145, 10, 92]-code), using

concatenation of two codes [i] based on
1. linear OA(16²⁴, 29, F₁₆, 22) (dual of [29, 5, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²⁴, 33, F₁₆, 22) (dual of [33, 9, 23]-code), using
    - extended algebraic-geometric code AG_e(F,10P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, 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(4¹²⁸, 69, F₄, 2, 84) (dual of [(69, 2), 10, 85]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4¹²⁸, 46, F₄, 3, 84) (dual of [(46, 3), 10, 85]-NRT-code)	[i]		OOA Folding