MinT - Information on Result #899337

Information on Result #899337

Linear OOA(25¹⁶, 8465, F₂₅, 2, 5) (dual of [(8465, 2), 16914, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25³, 651, F₂₅, 2, 2) (dual of [(651, 2), 1299, 3]-NRT-code), using
- appending kth column [i] based on linear OA(25³, 651, F₂₅, 2) (dual of [651, 648, 3]-code), using
  - Hamming code H(3,25) [i]
linear OOA(25¹³, 7814, F₂₅, 2, 5) (dual of [(7814, 2), 15615, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25¹³, 15628, F₂₅, 5) (dual of [15628, 15615, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. linear OA(25¹³, 15625, F₂₅, 5) (dual of [15625, 15612, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OA(25¹⁰, 15625, F₂₅, 4) (dual of [15625, 15615, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 25³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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(25⁶², 4202766, F₂₅, 2, 10) (dual of [(4202766, 2), 8405470, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(25⁶⁷, 4202766, F₂₅, 2, 11) (dual of [(4202766, 2), 8405465, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs