MinT - Information on Result #2694729

Information on Result #2694729

Linear OOA(5¹²⁵, large, F₅, 3, 9), using 4 times NRT-code embedding in larger space based on linear OOA(5¹¹³, 8388602, F₅, 3, 9) (dual of [(8388602, 3), 25165693, 10]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(5³¹, 4194301, F₅, 3, 4) (dual of [(4194301, 3), 12582872, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(5³¹, 8388602, F₅, 4) (dual of [8388602, 8388571, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(5³¹, large, F₅, 4) (dual of [large, large−31, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
2. linear OOA(5⁸², 4194301, F₅, 3, 9) (dual of [(4194301, 3), 12582821, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(5⁸², 8388602, F₅, 2, 9) (dual of [(8388602, 2), 16777122, 10]-NRT-code), using
    - trace code [i] based on linear OOA(25⁴¹, 4194301, F₂₅, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(25⁴¹, 8388602, F₂₅, 9) (dual of [8388602, 8388561, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁴¹, large, F₂₅, 9) (dual of [large, large−41, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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(5¹²⁶, large, F₅, 3, 9)	[i]		OOA Duplication
2	Linear OOA(5¹²⁷, large, F₅, 3, 9)	[i]		OOA Duplication