MinT - Information on Result #2517859

Information on Result #2517859

Linear OOA(25¹⁰³, large, F₂₅, 2, 13), using 8 times NRT-code embedding in larger space based on linear OOA(25⁸⁷, 8388602, F₂₅, 2, 13) (dual of [(8388602, 2), 16777117, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(25²⁶, 4194301, F₂₅, 2, 6) (dual of [(4194301, 2), 8388576, 7]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(25²⁶, 8388602, F₂₅, 6) (dual of [8388602, 8388576, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(25²⁶, large, F₂₅, 6) (dual of [large, large−26, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
2. linear OOA(25⁶¹, 4194301, F₂₅, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(25⁶¹, 8388602, F₂₅, 13) (dual of [8388602, 8388541, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(25⁶¹, large, F₂₅, 13) (dual of [large, large−61, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(25¹⁰⁴, large, F₂₅, 2, 13)	[i]		OOA Duplication