Codes with restricted overlaps : expandability, constructions, and bounds

Stanovnik, Lidija (avtor)

onsider a q-ary block code satisfying the property that no ℓ-letters long code-word’s prefix occurs as a suffix of any codeword for ℓ inside some interval. We determine a general upper bound on the maximum size of these codes and a tighter bound for codes where overlaps with lengths not exceeding k are prohibited. We then provide constructions for codes with various restrictions on overlap lengths and use them to determine lower bounds on the maximum sizes. In particular, we construct (1, k)-overlap-free codes where k ≥ n/2 and n denotes the block size, expand a known construction of (k, n − 1)-overlap-free codes, and combine the ideas behind both constructions to obtain (t$_1$, t$_2$)-overlap-free codes and codes that are simultaneously (1, k)- and (n − k, n − 1)-overlap-free for some k < n/2. In the case when overlaps of lengths between 1 and k are prohibited, we complete the characterisation of non-expandable codes initiated by Cai, Wang, and Feng (IEEE Trans Inf Theory, 2023).

• Jezik: Angleški jezik
• Ključne besede: overlap-free code, non-overlapping code, weakly mutually uncorrelated code
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FRI - Fakulteta za računalništvo in informatiko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: 26 str.
• Številčenje: Vol. , no.
• PID: 20.500.12556/RUL-168872
• UDK: 51:004
• ISSN pri članku: 1598-5865
• DOI: 10.1007/s12190-025-02441-z
• COBISS.SI-ID: 234691843
• Datum objave v RUL: 05.05.2025

Gradivo je del revije

• Naslov: Journal of Applied Mathematics and Computing : International Journal
• Skrajšan naslov: J. Appl. Math. Comput., Int. J.
• Založnik: Springer, Korean Society for Computational and Applied Mathematics
• ISSN: 1598-5865
• COBISS.SI-ID: 10636310

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Projekti

• Financer: ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: P2-0359
• Naslov: Vseprisotno računalništvo