MinT - Information on Result #682334

Information on Result #682334

Linear OA(5¹³⁹, 390675, F₅, 20) (dual of [390675, 390536, 21]-code), using constructionÂ X applied to C_e(20) âŠ‚ C_e(13) based on

linear OA(5¹²⁹, 390625, F₅, 21) (dual of [390625, 390496, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
linear OA(5⁸⁹, 390625, F₅, 14) (dual of [390625, 390536, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
linear OA(5¹⁰, 50, F₅, 5) (dual of [50, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹⁰, 52, F₅, 5) (dual of [52, 42, 6]-code), using
  - trace code [i] based on linear OA(25⁵, 26, F₂₅, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
    - extended Reedâ€“Solomon code RS_e(21,25) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
    - algebraic-geometric code AG(F,10P) 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+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(5¹⁴⁰, 390677, F₅, 20) (dual of [390677, 390537, 21]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
2	Linear OOA(5¹³⁹, 195337, F₅, 2, 20) (dual of [(195337, 2), 390535, 21]-NRT-code)	[i]	OOA Folding
3	Linear OOA(5¹³⁹, 130225, F₅, 3, 20) (dual of [(130225, 3), 390536, 21]-NRT-code)	[i]	OOA Folding