Algebraic structure of F_q-linear conjucyclic codes over finite field F_{q^2}

Recently, Abualrub et al. illustrated the algebraic structure of additive conjucyclic codes over F_4 (Finite Fields Appl. 65 (2020) 101678). In this paper, our main objective is to generalize their theory. Via an isomorphic map, we give a canonical bijective correspondence between F_q-linear additive conjucyclic codes of length n over F_{q^2} and q-ary linear cyclic codes of length 2n. By defining the alternating inner product, our proposed isomorphic map preserving the orthogonality can also be proved. From the factorization of the polynomial x^{2n}-1 over F_q, the enumeration of F_{q}-linear additive conjucyclic codes of length n over F_{q^2} will be obtained. Moreover, we provide the generator and parity-check matrices of these q^2-ary additive conjucyclic codes of length n

Investigation of the Freezing/Melting Process of Unsaturated Cement Paste by Low Temperature Calorimetry

Low temperature calorimetry (LTC) is usually applied to characterize the porosity of cement-based materials with a total water saturated state. By recording the heat flow of the sample at different testing temperatures, the ice content in the freezing and the melting process can be analyzed. In order to investigate the state of the water during the freezing/melting process of unsaturated porous materials, different from previous study, cement pastes of different moisture content are utilized and tested by LTC test. It is found that the nucleation temperature is independent of the degree of saturation in the range of 87%–100%, while the influence of the degree of saturation on the melting process is significant. For the melting process, the trough temperature increases with the decreasing degree of saturation, and water movement takes place in unsaturated samples during a freezing/melting cycle

On Euclidean, Hermitian and symplectic quasi-cyclic complementary dual codes

Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further, we determine the sufficient and necessary conditions for one-generator quasi-cyclic codes to be LCD codes involving Euclidean, Hermitian, and symplectic inner products. Finally, we constructed many Euclidean, Hermitian and symmetric LCD codes with excellent parameters, some improving the results in the literature. Remarkably, we construct a symplectic LCD $[28,6]_2$ code with symplectic distance $10$, which corresponds to an trace Hermitian additive complementary dual $(14,3,10)_4$ code that outperforms the optimal quaternary Hermitian LCD $[14,3,9]_4$ code