MinT - Information on Result #635134

Information on Result #635134

Linear OA(4¹⁹³, 205, F₄, 127) (dual of [205, 12, 128]-code), using concatenation of two codes based on

linear OA(16³⁵, 41, F₁₆, 31) (dual of [41, 6, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16³⁵, 45, F₁₆, 31) (dual of [45, 10, 32]-code), using
  - extended algebraic-geometric code AG_e(F,13P) [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(4¹⁹³, 205, F₄, 126) (dual of [205, 12, 127]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁹³, 205, F₄, 125) (dual of [205, 12, 126]-code)	[i]		Strength Reduction
3	Linear OA(4¹⁹², 204, F₄, 126) (dual of [204, 12, 127]-code)	[i]		Truncation
4	Linear OA(4¹⁹¹, 203, F₄, 125) (dual of [203, 12, 126]-code)	[i]
5	Linear OA(4¹⁹⁰, 202, F₄, 124) (dual of [202, 12, 125]-code)	[i]
6	Linear OA(4¹⁸⁹, 201, F₄, 123) (dual of [201, 12, 124]-code)	[i]
7	Linear OA(4¹⁸⁷, 199, F₄, 121) (dual of [199, 12, 122]-code)	[i]
8	Linear OA(4¹⁸⁶, 198, F₄, 120) (dual of [198, 12, 121]-code)	[i]
9	Linear OA(4¹⁸⁵, 197, F₄, 119) (dual of [197, 12, 120]-code)	[i]
10	Linear OA(4¹⁸⁴, 196, F₄, 118) (dual of [196, 12, 119]-code)	[i]
11	Linear OA(4¹⁸³, 195, F₄, 117) (dual of [195, 12, 118]-code)	[i]
12	Linear OA(4¹⁸², 194, F₄, 116) (dual of [194, 12, 117]-code)	[i]
13	Linear OOA(4¹⁹³, 102, F₄, 2, 127) (dual of [(102, 2), 11, 128]-NRT-code)	[i]		OOA Folding
14	Linear OOA(4¹⁹³, 68, F₄, 3, 127) (dual of [(68, 3), 11, 128]-NRT-code)	[i]		OOA Folding