MinT - Information on Result #2246776

Information on Result #2246776

Linear OA(5¹³⁵, 153, F₅, 86) (dual of [153, 18, 87]-code), using 3 times truncation based on linear OA(5¹³⁸, 156, F₅, 89) (dual of [156, 18, 90]-code), using

concatenation of two codes [i] based on
1. linear OA(25¹⁷, 26, F₂₅, 17) (dual of [26, 9, 18]-code or 26-arc in PG(16,25)), using
  - extended Reedâ€“Solomon code RS_e(9,25) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
  - algebraic-geometric code AG(F,4P) with 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+2P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
2. linear OA(5⁴, 6, F₅, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
  - extended Reedâ€“Solomon code RS_e(2,5) [i]
  - Simplex code S(2,5) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(5¹³⁹, 157, F₅, 86) (dual of [157, 18, 87]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(5¹⁴⁰, 158, F₅, 86) (dual of [158, 18, 87]-code)	[i]
3	Linear OA(5¹⁴¹, 159, F₅, 86) (dual of [159, 18, 87]-code)	[i]
4	Linear OA(5¹³⁸, 157, F₅, 86) (dual of [157, 19, 87]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(5¹³⁵, 76, F₅, 2, 86) (dual of [(76, 2), 17, 87]-NRT-code)	[i]	OOA Folding
6	Linear OOA(5¹³⁵, 51, F₅, 3, 86) (dual of [(51, 3), 18, 87]-NRT-code)	[i]	OOA Folding