arXiv subjects

Whan-Hyuk Choi

Publications and source records attributed to Whan-Hyuk Choi.

5 recordsLinked to original sources

arXiv2026

Algorithms of self-synchronizing single-deletion-correcting codes

This study explores the self-synchronization problem in DNA coding, specifically addressing single-deletion errors without using delimiters between codewords. We aim to identify the beginning of each codeword without using delimiters, enhancing the transmission efficiency. The motivation arises from the inefficiency of adding meaningless symbols as delimiters, decreasing the information rate. In addition, the historical context in biology, specifically Francis Crick's proposal of ``codes without commas'' for DNA sequences, inspires this investigation. We introduce a novel approach for correcting single-deletion errors in continuous transmissions without delimiters, distinguishing the beginning and end of each codeword. This approach is based on the properties of {\it complementary information set codes}, which is used to present an algorithm for {\it single-deletion correcting codes} with self-synchronizing capability. Accordingly, we present encoding and decoding algorithms for self-synchronizing single-deletion correcting DNA codes with concrete examples.

cs.IT↗

arXiv2024

New Constructions of Reversible DNA Codes

DNA codes have many applications, such as in data storage, DNA computing, etc. Good DNA codes have large sizes and satisfy some certain constraints. In this paper, we present a new construction method for reversible DNA codes. We show that the DNA codes obtained using our construction method can satisfy some desired constraints and the lower bounds of the sizes of some DNA codes are better than the known results. We also give new lower bounds on the sizes of some DNA codes of lengths $80$, $96$ and $160$ for some fixed Hamming distance $d$.

cs.IT↗

arXiv2022

Extending binary linear codes to self-orthogonal codes

Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal{C}$ $(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal{C})$. We extend this result by proposing a new method related to a special matrix, called the self-orthogonality matrix $SO_k$, obtained by shortening a Reed-Muller code $\mathcal R(2,k)$. Using this approach, we can extend binary linear codes to many optimal self-orthogonal codes of dimensions $5$ and $6$. Furthermore, we partially disprove the conjecture (Kim et al. (2021)) by showing that if $31 \le n \le 256$ and $n\equiv 14,22,29 \pmod{31}$, then there exist optimal $[n,5]$ codes which are self-orthogonal. We also construct optimal self-orthogonal $[n,6]$ codes when $41 \le n \le 256$ satisfies $n \ne 46, 54, 61$ and $n \not\equiv 7, 14, 22, 29, 38, 45, 53, 60 \pmod{63}$.

cs.IT↗

arXiv2021

Self-dual codes over $GF(q)$ with symmetric generator matrices

We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the best-known minimum weights of self-dual codes, which have not significantly improved for almost two decades. We focus on a class of self-dual codes, including double circulant codes. Using our method, called a `symmetric building-up' construction, we obtain many new self-dual codes over $GF(13)$ and $GF(17)$ and improve the bounds of best-known minimum weights of self-dual codes of lengths up to 40. Besides, we compute the minimum weights of quadratic residue codes that were not known before. These are: a [20,10,10] QR self-dual code over $GF(23)$, two [24,12,12] QR self-dual codes over $GF(29)$ and $GF(41)$, and a [32,12,14] QR self-dual codes over $GF(19)$. They have the highest minimum weights so far.

cs.IT↗

arXiv2021

An improved upper bound on self-dual codes over finite fields $GF(11), GF(19)$, and $GF(23)$

This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant codes. Using these methods, we construct an amount of symmetric self-dual codes over $GF(11)$, $GF(19)$, and $GF(23)$ of every length less than 42. We also find 153 {\it new} self-dual codes up to equivalence: they are $[32, 16, 12]$, $[36, 18, 13]$, and $[40, 20,14]$ codes over $GF(11)$, $[36, 18, 14]$ and $[40, 20, 15]$ codes over $GF(19)$, and $[32, 16, 12]$, $[36, 18, 14]$, and $[40, 20, 15]$ codes over $GF(23)$. They all have new parameters with respect to self-dual codes. Consequently, we improve bounds on the highest minimum distance of self-dual codes, which have not been significantly updated for almost two decades.

cs.IT↗