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Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound
Announce Type: new Abstract: In spite of the intensive study of cyclic codes and the recent construction of an infinite family of self-dual binary cyclic codes whose minimum distances have the square-root bound in IEEE Trans. 71, no. 4, 2025, it is still a 70-year-old open problem whether there is an infinite family of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound. This paper settles this long-standing open problem in coding theory...
Stability beyond Bounded Differences: Sharp Generalization Bounds under Finite $L_p$ Moments
arXiv:2606.06855v1 Announce Type: cross Abstract: While algorithmic stability is a central tool for understanding generalization of learning algorithms, existing high-probability guarantees typically rely on uniform boundedness or sub-Gaussian/sub-Weibull tail assumptions, which can be overly restrictive for modern settings with heavy-tailed or unbounded losses. We develop a stability-based framework that requires only a finite $L_p$ moment condition. Our first contribution is sharp...
Suboptimality bounds for trace-bounded SDPs enable a faster and scalable low-rank SDP solver SDPLR+
arXiv:2406.10407v3 Announce Type: replace-cross Abstract: Semidefinite programs (SDPs) and their solvers are powerful tools with many applications in machine learning and data science. Designing scalable SDP solvers is challenging because by standard the positive semidefinite decision variable is an $n \times n$ dense matrix, even though the input is often an $n \times n$ sparse matrix. However, the solution may not require a full-rank matrix, as shown by Barvinok and Pataki.
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...
Quantum Reservoir Computing and Risk Bounds
arXiv:2501.08640v2 Announce Type: replace Abstract: We propose a way to bound the generalisation errors of several classes of quantum reservoirs using the Rademacher complexity. We give specific, parameter-dependent bounds for two particular quantum reservoir classes. We analyse how the generalisation bounds scale with growing numbers of qubits.
State Observers for Linear Systems with Prescribed Residual Bounds
Announce Type: new Abstract: This paper presents a state observer design for continuous linear time-invariant (LTI) systems subject to unknown bounded disturbances, that enforces a prescribed bound on the observer residual. The proposed observer augments a continuous-time Luenberger observer with state resets, triggered when the norm of the residual equals a pre-specified bound. The reset map guarantees contraction of the residual at jump instants while preserving the uniform boundedness...
Quantum Time Lower Bounds by Permutation Invariance
arXiv:2606.05099v1 Announce Type: cross Abstract: Tight bounds on quantum sample complexity and quantum query complexity have been known for various computational problems in the literature, whereas tight bounds on quantum time complexity (i.e., the size of quantum circuits) remain unresolved. In this paper, we provide a framework to establish lower bounds on the quantum time complexity for testing permutation-invariant properties of quantum states, via a reduction from quantum sample...
Gaza-bound aid ship begins voyage from Sweden
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Complex Bounded Operators in Isabelle/HOL
Announce Type: replace Abstract: We present a formalization of bounded operators on complex vector spaces in Isabelle/HOL. Our formalization contains material on complex vector spaces (normed spaces, Banach spaces, Hilbert spaces) that complements and goes beyond the developments of real vectors spaces in the Isabelle/HOL standard library. We define the type of bounded operators between complex vector spaces (cblinfun) and develop the theory of unitaries, projectors, extension of bounded...
Texas-bound jet crashes during emergency landing in Dominican Republic
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