Related papers: Quaternary and Component-Binary Spreading Codes wi…
We propose a bit-flip descent method for optimizing binary spreading codes with large family sizes and long lengths, addressing the challenges of large-scale code design in GNSS and emerging PNT applications. The method iteratively flips…
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain…
In energy-time entanglement Quantum Key Distribution (QKD), two users extract a shared secret key from the arrival times (discretized as symbols) of entangled photon pairs. In prior work, Zhou et al. proposed a multi-level coding (MLC)…
A Z2Z4Q8-code is a non-empty subgroup of a direct product of copies of Z_2, Z_4 and Q_8 (the binary field, the ring of integers modulo 4 and the quaternion group on eight elements, respectively). Such Z2Z4Q8-codes are translation invariant…
In modern storage technologies, symbol-pair codes have emerged as a crucial framework for addressing errors in channels where symbols are read in overlapping pairs to guard against pair errors. A symbol-pair code that meets the…
The use of Space-Time Block Codes (STBCs) increases significantly the optimal detection complexity at the receiver unless the low-complexity decodability property is taken into consideration in the STBC design. In this paper we propose a…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
Self-dual codes have been studied actively because they are connected with mathematical structures including block designs and lattices and have practical applications in quantum error-correcting codes and secret sharing schemes.…
The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…
A subset $S$ of $\{0,1,...,2t-1\}^n$ is called a $t$-fold MDS code if every line in each of $n$ base directions contains exactly $t$ elements of $S$. The adjacency graph of a $t$-fold MDS code is not connected if and only if the…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
A code C is Z2Z4-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary…
Quantum error correction codes with non-local connections such as quantum low-density parity-check (qLDPC) incur lower overhead and outperform surface codes on large-scale devices. These codes are not applicable on current superconducting…
The evolution of multiple stellar systems can be driven by Kozai cycles and tidal friction (KCTF), which shrink the orbit of the inner binary. There is an interesting possibility that two close binaries on a common long-period orbit…
Low density parity check (LDPC) codes, initially discovered by Gallager, exhibit excellent performance in iterative decoding, approaching the Shannon limit. MDS array codes, with favorable algebraic structures, are codes suitable for…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…
Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of $[2^m+1, 2u-1, 2^m-2u+3]$ MDS codes for $1 \leq u \leq 2^{m-1}$, which are cyclic, reversible and BCH…
Double-close-binary quadruples (2+2 systems) are hierarchical systems of four stars where two short-period binary systems move around their common center of mass on a wider orbit. Using Gaia Early Data Release 3, we search for comoving…
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The…