MinT - Information on Result #839897

Information on Result #839897

Linear OOA(5¹¹³, 60, F₅, 2, 89) (dual of [(60, 2), 7, 90]-NRT-code), using OOA 2-folding based on linear OA(5¹¹³, 120, F₅, 89) (dual of [120, 7, 90]-code), using

discarding factors / shortening the dual code based on linear OA(5¹¹³, 121, F₅, 89) (dual of [121, 8, 90]-code), using
- 5 times truncation [i] based on linear OA(5¹¹⁸, 126, F₅, 94) (dual of [126, 8, 95]-code), using
  - constructionÂ X applied to C_e(93) âŠ‚ C_e(92) [i] based on
    1. linear OA(5¹¹⁸, 125, F₅, 94) (dual of [125, 7, 95]-code), using an extension C_e(93) of the primitive narrow-sense BCH-code C(I) with length 124Â = 5³âˆ’1, defining interval IÂ =Â [1,93], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 94 [i]
    2. linear OA(5¹¹⁷, 125, F₅, 93) (dual of [125, 8, 94]-code), using an extension C_e(92) of the primitive narrow-sense BCH-code C(I) with length 124Â = 5³âˆ’1, defining interval IÂ =Â [1,92], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 93 [i]
    3. linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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.

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(5¹¹³, 60, F₅, 2, 88) (dual of [(60, 2), 7, 89]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(5¹¹³, 60, F₅, 2, 87) (dual of [(60, 2), 7, 88]-NRT-code)	[i]
3	Linear OOA(5¹¹³, 60, F₅, 2, 86) (dual of [(60, 2), 7, 87]-NRT-code)	[i]
4	Linear OOA(5¹¹³, 60, F₅, 2, 85) (dual of [(60, 2), 7, 86]-NRT-code)	[i]
5	Linear OOA(5¹¹³, 60, F₅, 2, 84) (dual of [(60, 2), 7, 85]-NRT-code)	[i]