MinT - Information on Result #900094

Information on Result #900094

Linear OOA(25¹⁰³, 7940, F₂₅, 2, 28) (dual of [(7940, 2), 15777, 29]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25²⁴, 126, F₂₅, 2, 14) (dual of [(126, 2), 228, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,237P) [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(25⁷⁹, 7814, F₂₅, 2, 28) (dual of [(7814, 2), 15549, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁷⁹, 15628, F₂₅, 28) (dual of [15628, 15549, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
    1. linear OA(25⁷⁹, 15625, F₂₅, 28) (dual of [15625, 15546, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(25⁷⁶, 15625, F₂₅, 27) (dual of [15625, 15549, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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(25¹⁰³, 1134, F₂₅, 30, 28) (dual of [(1134, 30), 33917, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row