MinT - Information on Result #635239

Information on Result #635239

Linear OA(4²⁵⁷, 275, F₄, 163) (dual of [275, 18, 164]-code), using concatenation of two codes based on

linear OA(16⁴⁶, 55, F₁₆, 40) (dual of [55, 9, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁴⁶, 64, F₁₆, 40) (dual of [64, 18, 41]-code), using
  - algebraic-geometric code AG(F,23P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [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.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(4²⁵⁷, 275, F₄, 162) (dual of [275, 18, 163]-code)	[i]	Strength Reduction
2	Linear OA(4²⁵⁷, 275, F₄, 161) (dual of [275, 18, 162]-code)	[i]	Strength Reduction
3	Linear OA(4²⁵⁸, 276, F₄, 163) (dual of [276, 18, 164]-code)	[i]	Code Embedding in Larger Space
4	Linear OA(4²⁵⁹, 277, F₄, 163) (dual of [277, 18, 164]-code)	[i]	Code Embedding in Larger Space
5	Linear OA(4²⁵⁶, 274, F₄, 162) (dual of [274, 18, 163]-code)	[i]	Truncation
6	Linear OA(4²⁵⁵, 273, F₄, 161) (dual of [273, 18, 162]-code)	[i]
7	Linear OA(4²⁵⁴, 272, F₄, 160) (dual of [272, 18, 161]-code)	[i]
8	Linear OA(4²⁵³, 271, F₄, 159) (dual of [271, 18, 160]-code)	[i]
9	Linear OA(4²⁵¹, 269, F₄, 157) (dual of [269, 18, 158]-code)	[i]
10	Linear OA(4²⁵⁰, 268, F₄, 156) (dual of [268, 18, 157]-code)	[i]
11	Linear OOA(4²⁵⁷, 137, F₄, 2, 163) (dual of [(137, 2), 17, 164]-NRT-code)	[i]	OOA Folding