MinT - Information on Result #836349

Information on Result #836349

Linear OOA(5¹⁴⁰, 976578, F₅, 2, 19) (dual of [(976578, 2), 1953016, 20]-NRT-code), using OOA 2-folding based on linear OA(5¹⁴⁰, 1953156, F₅, 19) (dual of [1953156, 1953016, 20]-code), using

1 times code embedding in larger space [i] based on linear OA(5¹³⁹, 1953155, F₅, 19) (dual of [1953155, 1953016, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(15) [i] based on
  1. linear OA(5¹³⁶, 1953125, F₅, 19) (dual of [1953125, 1952989, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. linear OA(5¹⁰⁹, 1953125, F₅, 16) (dual of [1953125, 1953016, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  3. linear OA(5³, 30, F₅, 2) (dual of [30, 27, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
      - Hamming code H(3,5) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(5¹⁴², 976579, F₅, 2, 19) (dual of [(976579, 2), 1953016, 20]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(5¹⁴¹, 976578, F₅, 2, 19) (dual of [(976578, 2), 1953015, 20]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(5¹⁴⁰, 976578, F₅, 3, 19) (dual of [(976578, 3), 2929594, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Digital (121, 140, 976578)-net over F₅	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound