MinT - Information on Result #1550977

Information on Result #1550977

Linear OOA(5¹⁴⁷, 806594, F₅, 3, 21) (dual of [(806594, 3), 2419635, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(5¹⁴⁷, 806594, F₅, 2, 21) (dual of [(806594, 2), 1613041, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(5¹⁴⁷, 976568, F₅, 2, 21) (dual of [(976568, 2), 1952989, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁴⁷, 1953136, F₅, 21) (dual of [1953136, 1952989, 22]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(5¹⁴⁶, 1953135, F₅, 21) (dual of [1953135, 1952989, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
      1. linear OA(5¹⁴⁵, 1953125, F₅, 21) (dual of [1953125, 1952980, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. 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]
      3. linear OA(5¹, 10, F₅, 1) (dual of [10, 9, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(5¹⁴⁷, 201648, F₅, 27, 21) (dual of [(201648, 27), 5444349, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row