MinT - Information on Result #635118

Information on Result #635118

Linear OA(4¹⁹⁷, 215, F₄, 123) (dual of [215, 18, 124]-code), using concatenation of two codes based on

linear OA(16³⁴, 43, F₁₆, 30) (dual of [43, 9, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(16³⁴, 45, F₁₆, 30) (dual of [45, 11, 31]-code), using
  - extended algebraic-geometric code AG_e(F,14P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]
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 OA(4¹⁹⁷, 215, F₄, 122) (dual of [215, 18, 123]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁹⁷, 215, F₄, 121) (dual of [215, 18, 122]-code)	[i]		Strength Reduction
3	Linear OA(4¹⁹⁶, 214, F₄, 122) (dual of [214, 18, 123]-code)	[i]		Truncation
4	Linear OA(4¹⁹⁵, 213, F₄, 121) (dual of [213, 18, 122]-code)	[i]
5	Linear OA(4¹⁹⁴, 212, F₄, 120) (dual of [212, 18, 121]-code)	[i]
6	Linear OA(4¹⁹³, 211, F₄, 119) (dual of [211, 18, 120]-code)	[i]
7	Linear OA(4¹⁹¹, 209, F₄, 117) (dual of [209, 18, 118]-code)	[i]
8	Linear OA(4¹⁹⁰, 208, F₄, 116) (dual of [208, 18, 117]-code)	[i]
9	Linear OOA(4¹⁹⁷, 107, F₄, 2, 123) (dual of [(107, 2), 17, 124]-NRT-code)	[i]		OOA Folding