MinT - Information on Result #1550433

Information on Result #1550433

Linear OOA(5¹³⁷, 183438, F₅, 3, 22) (dual of [(183438, 3), 550177, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(5¹³⁷, 183438, F₅, 2, 22) (dual of [(183438, 2), 366739, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(5¹³⁷, 195316, F₅, 2, 22) (dual of [(195316, 2), 390495, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹³⁷, 390632, F₅, 22) (dual of [390632, 390495, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹³⁷, 390633, F₅, 22) (dual of [390633, 390496, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
      1. linear OA(5¹³⁷, 390625, F₅, 22) (dual of [390625, 390488, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(5¹²⁹, 390625, F₅, 21) (dual of [390625, 390496, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(5⁰, 8, F₅, 0) (dual of [8, 8, 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: 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		This result only	Method
1	Linear OOA(5¹³⁷, 45859, F₅, 27, 22) (dual of [(45859, 27), 1238056, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row