Optimal binary lcd codes
WebMar 2, 2024 · Binary is a base-2 number system representing numbers using a pattern of ones and zeroes. Early computer systems had mechanical switches that turned on to … WebNov 1, 2024 · Linear complementary dual codes (shortly LCD codes) are codes whose intersections with their dual codes are trivial. These codes were first introduced by …
Optimal binary lcd codes
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WebSep 6, 2024 · We call the LCD codes with parameters [n,k,d_ {LCD} (n, k)] optimal LCD codes. Binary optimal LCD codes have been classified up to length 16 in [ 12 ]. In [ 1 ], all values of d_ {LCD} (n, k) for n\le 24 are obtained and some classification results on LCD codes with … WebThe optimal binary LCD codes of length n≤16 are presented in [6] and all values of d LCD(n,k) for binary codes of lengths n≤40 are known [2]. Different methods have been used to study, construct and classify LCD codes with different parameters over different finite fields (see [6] and [5]). A method for constructing LCD binary codes via ...
WebIn this paper, the problem of finding LCD codes over the binary field is discussed. Many new codes and new bounds are presented, as well as a table of optimal LCD codes (or upper … WebMar 20, 2024 · We obtain binary LCD codes which have minimum weights two or three, and we also find some self-orthogonal codes meeting the Griesmer bound. As examples, we also present some (almost) optimal binary self-orthogonal codes and LCD distance optimal codes. Published in: IEEE Communications Letters ( Volume: 24 , Issue: 6 , June 2024 ) …
WebA binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary … WebOct 26, 2024 · Optimal Binary LCD Codes. Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. …
WebMar 17, 2024 · Furthermore, a binary [n,k,d] LCD code C is called LCD distance optimal if there is no [n,k,d+1] LCD code (that is, this LCD code has the largest minimum distance among [n,k] LCD codes for given length n …
WebLinear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. These codes were first introduced by … small white flowers on bushWebOct 26, 2024 · Optimal Binary LCD Codes Stefka Bouyuklieva Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. These codes were first introduced by Massey in 1964. Nowadays, LCD codes are extensively studied in the literature and widely applied in data storage, … small white flowers namesWebJan 1, 2024 · The largest minimum weights among all binary LCD [n, k] codes were partially determined in [3,8,16,17,25,28] for n ≤ 40. It is worth noting that there are many unknowns in [8] and [28]. The... hiking trails scotland highlandshttp://info.fmi.shu-bg.net/skin/pfiles/3_9_p13_c2_lcd_v0.5.pdf hiking trails scranton paWebOct 26, 2024 · Optimal Binary LCD Codes Stefka Bouyuklieva Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual … small white flowers in lawnWebThe optimal binary LCD codes of length n≤16 are presented in [6] and all values of d LCD(n,k) for binary codes of lengths n≤40 are known [2]. Different methods have been … small white flowers on stemWebJun 10, 2024 · We show that all odd-like binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes can be constructed using the modified methods. We also construct a lot of optimal binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes, which improve the known lower bounds on the largest minimum weights. small white flowers smell like honey