MinT - Information on Result #638112

Information on Result #638112

Linear OA(5¹¹⁴, 130, F₅, 75) (dual of [130, 16, 76]-code), using concatenation of two codes based on

linear OA(25¹⁸, 26, F₂₅, 18) (dual of [26, 8, 19]-code or 26-arc in PG(17,25)), using
- extended Reedâ€“Solomon code RS_e(8,25) [i]
- algebraic-geometric code AG(F, Q+2P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
- algebraic-geometric code AG(F, Q+1P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
linear OA(5³, 5, F₅, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,5) or 5-cap in PG(2,5)), using
- Reedâ€“Solomon code RS(2,5) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(5¹¹⁴, 130, F₅, 74) (dual of [130, 16, 75]-code)	[i]	Strength Reduction
2	Linear OA(5¹¹⁵, 131, F₅, 75) (dual of [131, 16, 76]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(5¹¹⁶, 132, F₅, 75) (dual of [132, 16, 76]-code)	[i]
4	Linear OA(5¹¹⁷, 133, F₅, 75) (dual of [133, 16, 76]-code)	[i]
5	Linear OA(5¹¹³, 129, F₅, 74) (dual of [129, 16, 75]-code)	[i]	Truncation
6	Linear OA(5¹¹², 128, F₅, 73) (dual of [128, 16, 74]-code)	[i]
7	Linear OA(5¹¹¹, 127, F₅, 72) (dual of [127, 16, 73]-code)	[i]
8	Linear OA(5¹¹⁰, 126, F₅, 71) (dual of [126, 16, 72]-code)	[i]
9	Linear OA(5¹¹⁹, 136, F₅, 75) (dual of [136, 17, 76]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
10	Linear OOA(5¹¹⁴, 65, F₅, 2, 75) (dual of [(65, 2), 16, 76]-NRT-code)	[i]	OOA Folding
11	Linear OOA(5¹¹⁴, 43, F₅, 3, 75) (dual of [(43, 3), 15, 76]-NRT-code)	[i]	OOA Folding