MinT - Information on Result #683127

Information on Result #683127

Linear OA(5¹¹⁵, 3174, F₅, 25) (dual of [3174, 3059, 26]-code), using constructionÂ X applied to C_e(25) âŠ‚ C_e(16) based on

linear OA(5¹⁰¹, 3125, F₅, 26) (dual of [3125, 3024, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
linear OA(5⁶⁶, 3125, F₅, 17) (dual of [3125, 3059, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
linear OA(5¹⁴, 49, F₅, 7) (dual of [49, 35, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹⁴, 52, F₅, 7) (dual of [52, 38, 8]-code), using
  - trace code [i] based on linear OA(25⁷, 26, F₂₅, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
    - extended Reedâ€“Solomon code RS_e(19,25) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
    - algebraic-geometric code AG(F,9P) 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,6P) with 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		This result only	Method
1	Linear OOA(5¹¹⁵, 1587, F₅, 2, 25) (dual of [(1587, 2), 3059, 26]-NRT-code)	[i]		OOA Folding
2	Linear OOA(5¹¹⁵, 1058, F₅, 3, 25) (dual of [(1058, 3), 3059, 26]-NRT-code)	[i]		OOA Folding