• Journal of the Korea Fashion and Costume Design Association
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• v.6 no.1
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• pp.34-45
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• 2004

The purpose of the study was to investigate weaving, traditional dyeing, fiber material, pattern how carpet developing according to Turkey area for using the data that can rear to the export strategic industry for carpet production and development that is correct in culture. The result are followed: 1) Life of the age was expressed in color and pattern using according to geographical environment, climate, lifestyle, religion etc. 2) In the case of weaving, there is Kilim, Soumak that appears only weft on the surface as plane weaving without knot and carpet of knotted pile weaving and knot of carpet is duplex knot difference with carpet of the other country. 3) In the case of textile material, there is use most wool fiber that can get easily from breeded sheep by nomads. 4) In the case of dyeing, did the local traditional color to use dye extracting in dyeing material that can get easily in the area. Red that can extract in madder that can get easily in which area of Turkey, dark navy blue of indigo dye that indigo plant fermentation and cream beige that is wool's natural color were exposed representative traditional color of Turkey carpet. 5) Pattern was advanced uniquely as culture of the area; weaving person's sensitivity and desire are reflected through centuries. Amulet, riches ＆ honors, fecundity and happiness appeared most pattern in any area.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.571-595
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• 2021

In this paper we study the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, where u^k = 0 and p is a prime. A ℤ_pℤ_p[u]/k>-linear code of length (r + s) is an R_k-submodule of ℤ^r_p × R^s_k with respect to a suitable scalar multiplication, where R_k = ℤ_p[u]/k>. Such a code can also be viewed as an R_k-submodule of ℤ_p[x]/r - 1> × R_k[x]/s - 1>. A new Gray map has been defined on ℤ_p[u]/k>. We have considered two cases for studying the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, and determined the generator polynomials and minimal spanning sets of these codes in both the cases. In the first case, we have considered (r, p) = 1 and (s, p) ≠ 1, and in the second case we consider (r, p) = 1 and (s, p) = 1. We have established the MacWilliams identity for complete weight enumerators of ℤ_pℤ_p[u]/k>-linear codes. Examples have been given to construct ℤ_pℤ_p[u]/k>-cyclic codes, through which we get codes over ℤ_p using the Gray map. Some optimal p-ary codes have been obtained in this way. An example has also been given to illustrate the use of MacWilliams identity.