DNA data storage is a highly emerging technology of storing large amount of data in a small volume for a long period of time. However, synthesis of DNA sequences come with a cost that depends on the number of nucleotides present in it. An efficient algorithm to store large amount of data in small number of nucleotides has been proposed which uses minimum-variance Huffman coding. The DNA sequences generated follow GC-constraint and run-length constraint of at most 1. Texts have been stored in lossless manner. Images have been stored in both lossless and lossy manner. In either of the cases, a high code-rate has been attained, thus implying good compression and reduction in cost of synthesis.

The ring R = Fpm + uFpm has precisely pm(pm–1) units, which are of the forms γ and α+uβ, where 0 ≠ α,β,γ ∈ Fpm. Using generator polynomial structures of constacyclic codes of length ps over R, the Hamming and symbol-pair distance distributions of all such codes are completely determined. As examples, we provide some good codes with better parameters than the known ones.

Symbol-pair codes are used to protect against symbol-pair errors in high density data storage systems. One of the most important tasks in symbol-pair coding theory is to design MDS codes. MDS symbol-pair codes are optimal in the sense that such codes attain the Singleton bound. In this paper, a new class of MDS symbol-pair codes with code-length $5p$ and optimal pair distance of 7 is established. It is shown that for any prime $p \equiv 1 \pmod 5$ , we can always construct four $p$ -ary MDS symbol-pair cyclic codes of length $5p$ of largest possible pair distance 7. We also completely determined all MDS symbol-pair and MDS $b$ -symbol codes of length $p^{s}$ and $2p^{s}$ over $\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ by filling in some missing cases, and rectifying some gaps in Type 3 codes of recent papers. As an applications of our results, we use MAGMA to provide many examples of new MDS codes over $\mathbb F_{p^{m}}$ and $\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ .

This paper introduces a variant of the McEliece cryptosystem and employs the ( C ₁ , C ₁ + C ₂ )-construction to generate a new code from two arbitrary linear codes. We propose an efficient hard-decision decoding algorithm for linear codes derived from the ( C ₁ , C ₁ + C ₂ )-construction and integrate them into the McEliece framework. The security of the cryptosystem varies based on the specific codes used in the ( C ₁ , C ₁ + C ₂ )-construction. Our proposed variant achieves a good level of security with approximately the same key size compared to one of the classic McEliece candidates of the National Institute of Standards and Technology (NIST) [1] standardization process. Specifically, we demonstrate a 25% key size reduction for our proposed parameters compared to one of the 256-bit secured classic McEliece parameters.

The goal of image cryptosystems is to protect image transmission when there are network adversaries present. To ensure secrecy, images are subject to encryption to produce unintelligible cipher images; the techniques used for this process differ significantly from those applied to text data. The majority of the cryptosystems consider complicated or confusion–diffusion architectures that change and permute the values of the pixels. These frequently entail binary operations like bitwise \(\texttt{XOR}\), addition–subtraction, DNA operations, etc, and are carried out utilizing chaotic maps, each having certain limitations. This paper employs a non-linear binary function applicable to traditional and DNA techniques for color image cryptosystems. In the proposed method, each of the color components of the image follows some steps which start with inter-channel mixing and mix rows, taking the values from the initial vector and mixing it. Arnold’s cat map algorithm is then applied to shuffle the pixels, and a novel spiral mixing of the pixels is applied in four different directions to prevent the differential attack. Finally, encoding, substitution, and decoding based on DNA is carried out. A multiple collapse chaotic map is used to derive initialization vectors, rule maps, and DNA substitution maps which are used in encoding and decoding processes. Experimental results and analysis show that the proposed cryptosystem results in cipher images that are resistant to different types of cryptographic attacks, thereby providing a secure color image encryption and decryption scheme.