MinT - Information on Result #899981

Information on Result #899981

Linear OOA(25⁹², 7940, F₂₅, 2, 24) (dual of [(7940, 2), 15788, 25]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25²², 126, F₂₅, 2, 12) (dual of [(126, 2), 230, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,239P) [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
  - the Hermitian function field over F₂₅ [i]
linear OOA(25⁷⁰, 7814, F₂₅, 2, 24) (dual of [(7814, 2), 15558, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷⁰, 15628, F₂₅, 24) (dual of [15628, 15558, 25]-code), using
  - constructionÂ X applied to C_e(23) âŠ‚ C_e(22) [i] based on
    1. linear OA(25⁷⁰, 15625, F₂₅, 24) (dual of [15625, 15555, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
    2. linear OA(25⁶⁷, 15625, F₂₅, 23) (dual of [15625, 15558, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(25⁰, 3, F₂₅, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(25⁹², 1323, F₂₅, 26, 24) (dual of [(1323, 26), 34306, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row