In this paper , we will more deeply research on the base of the works , the first part , we give the summarize for the condition and the significance . the second part , we give the preparation knowledge to the whole paper ; the third part , we research the lower and upper bound of the generalized hamming weights for the linear codes ; include d ( r , n , k ) bound , the finite sum representation of the lower and upper bound function of generalized hamming weights for linear codes , generalized griesmer bounds ; the 4 - th part , research the definition , the property of the r - th generalized weights for the non - linear codes and non - linear constant codes , and give the expression of the generalized weight of binary ( n , m , d ) non - linear codes ; the 5 - th part , research the weight hierarchy of linear codes and non - linear codes , for example , necessary condition and sufficient condition , the 6 - th part , we research the expression of the r - th generalized hamming weights of reseaval classes codes 本文在已有的基礎(chǔ)之上作了進(jìn)一步的探討,第一章綜述了廣義hamming重量的現(xiàn)狀和意義;第二章給出了全文的預(yù)備知識(shí);第三章研究了線性碼的廣義hamming重量的一些上下界;包括d ( r , n , k )界,上下限函數(shù)有限和表達(dá)式,廣義griesmer界;第四章討論了非線性碼及非線性等重碼的廣義hamming重量的定義、性質(zhì),給出了2元( n , m , d )非線性碼的第r廣義hamming重量的表達(dá)式;第五章研究了線性碼、非線性碼的重量譜系;第六章給出了幾類碼的廣義hamming重量的表達(dá)式,這些碼包括直和碼( directsumcodes ) 、笛卡爾積碼( cartesianproductcodes ) 、張量積碼( tensorproductcodes ) 、延長(zhǎng)hamming碼。
( 3 ) by means of expanding the aperture function into a finite sum of complex gaussian functions , the propagation of fgbs through a paraxial optical abcd system with hard - edged aperture is studied , and the approximate closed - form equations of apertured fgbs are obtained for the first time . the results obtained by using the approximate closed - form equation and collins formula are compared , and the condition under which the approximate closed - form equation is applicable is analyzed ( 3 )利用光闌函數(shù)的復(fù)高斯函數(shù)展開(kāi)法對(duì)截?cái)嗥巾敻咚构馐膫鬏斪髁搜芯?,首次得到了截?cái)嗥巾敻咚构馐诮Sabcd光學(xué)系統(tǒng)中傳輸時(shí)的近似解析傳輸公式,通過(guò)比較用近似傳物公式和colhns公式直接數(shù)值積分所得的結(jié)果,得出了近似公式的適用范圍。
finite: adj. 有限的;【語(yǔ)法】限定的;【數(shù)學(xué)】有窮的,有盡的 ...sum: n. 1.總數(shù),總計(jì),總額;【數(shù)學(xué)】和。 2.〔the ...finite sum formula: 有限項(xiàng)和公式locally finite sum: 局部有限和orthogonal for finite sum: 選點(diǎn)正交finite: adj. 有限的;【語(yǔ)法】限定的;【數(shù)學(xué)】有窮的,有盡的。 n. 〔the finite〕 有限(性); 〔集合詞〕有限物。 adv. -ly ,-ness n. a in sum: 簡(jiǎn)言之.一言以蔽之in sum: 大體上, 總之; 扼要地說(shuō); 簡(jiǎn)而言之; 總而言之; 總言之; 總之,簡(jiǎn)言之not sum: 非和sum: SUM =surface-to-underwater missile 艦對(duì)水下導(dǎo)彈[飛彈]。 n. 1.總數(shù),總計(jì),總額;【數(shù)學(xué)】和。 2.〔the sum〕概略,大要,要點(diǎn)。 3.款項(xiàng),金額。 4.算術(shù)(題);運(yùn)算,計(jì)算。 5.【詩(shī)】頂點(diǎn),絕頂,極點(diǎn)。 sum remainder, product, quotient 和,差,積,商。 a sum total 總計(jì),合計(jì)。 the sum of his opinions 他的意見(jiàn)的要點(diǎn)。 a good [considerable, round] sum一大[整]筆錢。 a large [small] sum of 巨[小]額的,大[小]量的。 be good at sums 算術(shù)好。 do [work, make] a sum(s) 計(jì)算,做算術(shù)題。 in sum大體上,一言以蔽之,總之。 the sum (and substance) 要點(diǎn)。 the sum of things (最高的)公共利益;宇宙。 vt. (-mm-) 合計(jì),總計(jì);總結(jié),總括,概括。 vi. 總計(jì)(into, to);(法官聽(tīng)原告、被告陳述后)概括要點(diǎn) (up)。 Contributions sums to several thousand dollars. 捐款總計(jì)達(dá)數(shù)千美元。 sum up 總計(jì),總結(jié);總起來(lái)說(shuō)。 sum up experiences 總結(jié)經(jīng)驗(yàn)。 sum to: 共計(jì); 項(xiàng)和sum-: 前綴 〔用于 m 前〕=sub-. finite elemente finite elements: 有限元素difference; finite: 有限差分endlich finite: 有限的finite additivity: 有限可加性finite aggregate: 有限集合finite algebra: 有限代數(shù)finite alphabet: 有限字母, 有窮字母finite amount: 有限量finite amplitude: 有限振幅finite angle: 有限角finite aperture: 有限孔徑finite aquifer: 有限含水層finite automat: 有限自動(dòng)機(jī)