MinT - Information on Result #683115

Information on Result #683115

Linear OA(5¹⁰⁰, 3169, F₅, 22) (dual of [3169, 3069, 23]-code), using constructionÂ X applied to C_e(21) âŠ‚ C_e(13) based on

linear OA(5⁸⁶, 3125, F₅, 22) (dual of [3125, 3039, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
linear OA(5⁵⁶, 3125, F₅, 14) (dual of [3125, 3069, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
linear OA(5¹⁴, 44, F₅, 7) (dual of [44, 30, 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		Method
1	Linear OA(5¹⁰¹, 3170, F₅, 22) (dual of [3170, 3069, 23]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(5¹⁰⁰, 1584, F₅, 2, 22) (dual of [(1584, 2), 3068, 23]-NRT-code)	[i]	OOA Folding
3	Linear OOA(5¹⁰⁰, 1056, F₅, 3, 22) (dual of [(1056, 3), 3068, 23]-NRT-code)	[i]	OOA Folding