MinT - Information on Result #2504539

Information on Result #2504539

Linear OOA(5¹⁴⁸, 7838, F₅, 2, 28) (dual of [(7838, 2), 15528, 29]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(5¹⁴⁶, 7837, F₅, 2, 28) (dual of [(7837, 2), 15528, 29]-NRT-code), using

OOA 2-folding [i] based on linear OA(5¹⁴⁶, 15674, F₅, 28) (dual of [15674, 15528, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5¹⁴⁵, 15673, F₅, 28) (dual of [15673, 15528, 29]-code), using
  - constructionÂ X applied to C_e(27) âŠ‚ C_e(20) [i] based on
    1. linear OA(5¹³³, 15625, F₅, 28) (dual of [15625, 15492, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    2. linear OA(5⁹⁷, 15625, F₅, 21) (dual of [15625, 15528, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(5¹², 48, F₅, 6) (dual of [48, 36, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(5¹², 62, F₅, 6) (dual of [62, 50, 7]-code), using
        the cyclic code C(A) with length 62Â | 5³âˆ’1, defining set AÂ =Â {4,8,11,17}, and minimum distance dÂ â‰¥ |{8,11,14,…,23}|+1Â =Â 7 (BCH-bound) [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		This result only	Method
1	Linear OOA(5¹⁴⁹, 7838, F₅, 2, 28) (dual of [(7838, 2), 15527, 29]-NRT-code)	[i]		OOA Duplication