A Quaternary Code Correcting a Burst of at Most Two Deletion or Insertion Errors in DNA Storage

Due to the properties of DNA data storage, the errors that occur in DNA strands make error correction an important and challenging task. In this paper, a new code design of quaternary code suitable for DNA storage is proposed to correct at most two consecutive deletion or insertion errors. The decoding algorithms of the proposed codes are also presented when one and two deletion or insertion errors occur, and it is proved that the proposed code can correct at most two consecutive errors. Moreover, the lower and upper bounds on the cardinality of the proposed quaternary codes are also evaluated, then the redundancy of the proposed code is provided as roughly 2log48n.

Some Constacyclic Codes over ℤ4[u]/〈u2〉,, New Gray Maps, and New Quaternary Codes

In this paper, we study λ-constacyclic codes over the ring R = ℤ4 + uℤ4, where u2 = 0, for λ =1 + 3u and 3 + u. We introduce two new Gray maps from R to [Formula: see text] and show that the Gray images of λ-constacyclic codes over R are quasi-cyclic over ℤ4. Moreover, we present many examples of λ-constacyclic codes over R whose ℤ4-images have better parameters than the currently best-known linear codes over ℤ4.

Entanglement-assisted quantum codes from quaternary codes of dimension five

Maximal-entanglement entanglement-assisted quantum error-correcting codes (EAQE-CCs) can achieve the EA-hashing bound asymptotically and a higher rate and/or better noise suppression capability may be achieved by exploiting maximal entanglement. In this paper, we discussed the construction of quaternary zero radical (ZR) codes of dimension five with length [Formula: see text]. Using the obtained quaternary ZR codes, we construct many maximal-entanglement EAQECCs with very good parameters. Almost all of these EAQECCs are better than those obtained in the literature, and some of these EAQECCs are optimal codes.