Related papers: Bounds for complexity of syndrome decoding for pos…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
The Learning Parity with Noise (LPN) problem underlines several classic cryptographic primitives. Researchers have attempted to demonstrate the algorithmic hardness of this problem by finding reductions from the decoding problem of linear…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
In this work, we study the problem of list decoding of insertions and deletions. We present a Johnson-type upper bound on the maximum list size. The bound is meaningful only when insertions occur. Our bound implies that there are binary…
In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…
In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We…
We give a recursive decoding algorithm for projective Reed-Muller codes making use of a decoder for affine Reed-Muller codes. We determine the number of errors that can be corrected in this way, which is the current highest for decoders of…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Permutation decoding is a technique which involves finding a subset $S$, called PD-set, of the permutation automorphism group of a code $C$ in order to assist in decoding. An explicit construction of $\left \lfloor{\frac{2^m-m-1}{1+m}}…
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…
We study a class of gauge fixings of the Bacon-Shor code at the circuit level, which includes a subfamily of generalized surface codes. We show that for these codes, fault tolerance can be achieved by direct measurements of the stabilizers.…
We propose the first non-trivial generic decoding algorithm for codes in the sum-rank metric. The new method combines ideas of well-known generic decoders in the Hamming and rank metric. For the same code parameters and number of errors,…
We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order $k$ cannot have very small…
One of the main weakness of the family of centralizer codes is that its length is always $n^2$. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form $nk$.…
In realistic stabiliser-based quantum error correction there are many ways in which real physical systems deviate from simple toy models of error. Stabiliser measurements may not always be deterministic or may suffer from erasure errors,…
The class of poset metrics is very large and contains some interesting families of metrics. A family of metrics, based on posets which are formed from disjoint chains which have the same size, is examined. A necessary and sufficient…
We show that for (systematic) linear codes the time complexity of unique decoding is O(n^{2}q^{nRH(delta/2/R)}) and the time complexity of minimum distance decoding is O(n^{2}q^{nRH(delta/R)}). The proposed algorithm inspects all error…
The generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in…