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In this paper, all of the conjectures in Aydin et al. (2022) [6] are settled: some proven correct, some proven correct with a modification, and some disproven, involving the equivalence and duality of polycyclic codes associated with trinomials. We also give methods to construct isodual and self-dual polycyclic codes, and study the self-orthogonal and dual-containing polycyclic codes over F 2. [ABSTRACT FROM AUTHOR]

The codes in the title are studied with respect to existence, enumeration and asymptotic performance. Their Gray images are shown to satisfy a modified Gilbert-Varshamov bound. Explicit counting formulas are derived. Examples of modest lengths are given where Gray images of LCD Z 4 -codes outperform the best known binary linear LCD codes. [ABSTRACT FROM AUTHOR]

In this paper 1 , we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis. [ABSTRACT FROM AUTHOR]

We first define a new Gray map from R = Z 4 + u Z 4 to Z 4 2 , where u 2 = 1 and study ( 1 + 2 u ) -constacyclic codes over R . Also of interest are some properties of ( 1 + 2 u ) -constacyclic codes over R . Considering their Z 4 images, we prove that the Gray images of ( 1 + 2 u ) -constacyclic codes of length n over R are cyclic codes of length 2 n over Z 4 . In many cases the latter codes have better parameters than those in the online database of Aydin and Asamov. We also give a corrected version of a table of new cyclic R -codes published by Özen et al. [7] . [ABSTRACT FROM AUTHOR]