MinT - Information on Result #906441

Information on Result #906441

Linear OOA(5¹³⁰, 4194426, F₅, 2, 14) (dual of [(4194426, 2), 8388722, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁹, 125, F₅, 2, 7) (dual of [(125, 2), 231, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹, 25, F₅, 2, 1) (dual of [(25, 2), 49, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(5¹, 25, F₅, 2, 1) (dual of [(25, 2), 49, 2]-NRT-code) (see above)
  3. linear OOA(5³, 25, F₅, 2, 2) (dual of [(25, 2), 47, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
        Hamming code H(3,5) [i]
  4. linear OOA(5⁴, 25, F₅, 2, 3) (dual of [(25, 2), 46, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5⁴, 26, F₅, 2, 3) (dual of [(26, 2), 48, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
        ovoid in PG(3,Â 5) [i]
  5. linear OOA(5¹⁰, 25, F₅, 2, 7) (dual of [(25, 2), 40, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 10, 25)-net over F₅, using
      - linear code embedding found in a computer search [i]
linear OOA(5¹¹¹, 4194301, F₅, 2, 14) (dual of [(4194301, 2), 8388491, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹¹¹, 8388602, F₅, 14) (dual of [8388602, 8388491, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹¹¹, large, F₅, 14) (dual of [large, large−111, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(5¹³¹, 4194426, F₅, 2, 14) (dual of [(4194426, 2), 8388721, 15]-NRT-code)	[i]		OOA Duplication