Singleton Bound
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
The Arithmetic Singleton Bound on the Hamming Distances of Simple-rooted Constacyclic Codes over Finite Fields
Announce Type: replace Abstract: In this work, We introduce a new upper bound on the Hamming distance of simple-root constacyclic codes over finite fields, which we call the arithmetic Singleton bound. The main technical tool is the notion of a multiple equal-difference (MED) representation. Via the MED representations of the defining set of the generator polynomial of a simple-root constacyclic code, we obtain a family of upper bounds on its Hamming distance, among which the weakest one...
Constructions of Quantum $(r,\delta)$-LRCs from cyclic codes
Announce Type: new Abstract: Classical $(r,\delta)$ locally recoverable codes (LRCs) play a central role in distributed data storage systems as they enable an efficient recovery from erasures by accessing a small number of surviving symbols. Motivated by their prospective use in future quantum data storage and by recent theoretical progress on quantum locally recoverable codes (qLRCs), we investigate the construction of qLRCs from classical cyclic $(r,\delta)$-LRCs. Our approach identifies...
Quantum Hierarchical Locally Recoverable Codes
arXiv:2606.06736v1 Announce Type: new Abstract: Quantum locally recoverable codes (QLRCs) have recently gained attention as a framework for achieving efficient quantum storage with local recovery capabilities. Analogous to their classical counterparts, QLRCs allow a lost qudit to be reconstructed using only a small subset of other qudits, thereby reducing the resource and operational overhead in recovery.
An Explicit Scott-Type Bound for Absolutely Maximally Entangled States with Arbitrary Defect
arXiv:2606.01943v1 Announce Type: cross Abstract: Absolutely maximally entangled (AME) states and, more generally, $k$-uniform states in $(\C^q)^{\otimes n}$ are central objects in multipartite entanglement theory, with applications to quantum secret sharing, quantum masking, and quantum error correction. In the extremal case $k=\lfloor n/2\rfloor$, Scott (2004) proved a sharp nonexistence bound showing that AME states cannot exist once the number of parties $n$ exceeds a threshold of order...
The Cascade Log: Reference-Stable Windowing over Tiered Append Sequences
Announce Type: new Abstract: A long-running append-mostly sequence, such as an edit log, event store, or versioned working set, is usually tiered into a bounded hot stratum and colder folded summaries. This saves memory but breaks stable references: a handle minted while a record is hot may later be resolved after the record has moved into a digest, after it has been superseded, or while a fold is in flight. We define the resulting cross-tier anomalies--dangling, stale, corrupt, and...
Future Power Rankings: How all 68 Power 4 college football teams stack up
Projecting a college football program's future is harder than ever. Rosters and fortunes change dramatically and championship pathways are more open than ever. The assets that make a program great in 2026 might not be there in 2027.