MinT - Information on Result #2694845

Information on Result #2694845

Linear OOA(5¹¹⁵, 4194302, F₅, 3, 12) (dual of [(4194302, 3), 12582791, 13]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(5¹¹², 4194301, F₅, 3, 12) (dual of [(4194301, 3), 12582791, 13]-NRT-code), using

OOA 2-folding [i] based on linear OOA(5¹¹², 8388602, F₅, 2, 12) (dual of [(8388602, 2), 16777092, 13]-NRT-code), using
- trace code [i] based on linear OOA(25⁵⁶, 4194301, F₂₅, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(25⁵⁶, 8388602, F₂₅, 12) (dual of [8388602, 8388546, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(25⁵⁶, large, F₂₅, 12) (dual of [large, large−56, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, 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(5¹¹⁶, 4194302, F₅, 3, 12) (dual of [(4194302, 3), 12582790, 13]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(5¹¹⁷, 4194302, F₅, 3, 12) (dual of [(4194302, 3), 12582789, 13]-NRT-code)	[i]		OOA Duplication