ÕªÒª£º ÏÖÔÚ½éÉܸêÀ³ÓÚ 1949 Äê·¢ÏÖµÄÁ½¸öÍêÈ«ÏßÐÔÂë, ºóÈ˳Æ×÷¸êÀ³Âë. Ò»¸ö \(p\) ÔªÍêÈ«ÂëµÄ×îС¾àÀë \(d\) Ò»¶¨ÊÇÆæÊý \(2 l+1\) (\(1.3\) ½ÚÏ°Ìâ \(6\))²¢ÇÒ´ïµ½ººÃ÷½ç,¼´ \[p^{n-k}=\sum_{i=0}^l(p-1)^i\binom{n}{i}, \] ÔĶÁÈ«ÎÄ
posted @ 2024-07-03 02:41 Pizixsr ÔĶÁ(1) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º ¶¨Òå 1 Éè \(\boldsymbol{a}=\left(a_1, \cdots, a_n\right)\) ºÍ \(\boldsymbol{b}=\) \(\left(b_1, \cdots, b_n\right)\) ÊÇ \(F_p^n\) ÖеÄÏòÁ¿. \(\boldsymbol{a}\) ºÍ ÔĶÁÈ«ÎÄ
posted @ 2024-07-02 17:32 Pizixsr ÔĶÁ(1) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º ±¾½ÚµÄÄ¿±êÊǸø³öһϵÁÐÏßÐÔÍêÈ«Âë, ½Ð×öººÃ÷Âë $(Hamming~code)$. Ê×ÏÈ,a56爆大奖在线娱乐ÃÇÓÐÁ½Ààƽ·²µÄÍêÈ«ÏßÐÔÂ룺 \((1)\) \(q\) ÔªÏßÐÔÂë \([n, n, 1]\), ¼´ \(C=\mathrm{F}_q^n\) ¡£Ò×ÖªÕâÊÇÍêÈ«Âë¡£ \((2)\) ¶ÔÓÚ \(n=2 l+1, q ÔĶÁÈ«ÎÄ
posted @ 2024-07-01 17:45 Pizixsr ÔĶÁ(1) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º ¶¨Òå 1 Ò»¸öÂ볤Ϊ \(n\) µÄ \(p\) ÔªÂë \(C\) ½Ð×öÏßÐÔÂë, ÊÇÖ¸ \(C\) ÊÇÏòÁ¿¿Õ¼ä \(F_p^n\) µÄÏòÁ¿×Ó¿Õ¼ä,¼´ \(C\) Âú×ãÈçϵÄÐÔÖÊ: ¶ÔÓÚ \(F_p\) ÖÐÈa56爆大奖在线娱乐âÔªËØ \(\alpha\)ºÍ \(\beta\), Èç¹û \(\boldsymbol{c}_ ÔĶÁÈ«ÎÄ
posted @ 2024-06-30 23:24 Pizixsr ÔĶÁ(1) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º ¶¨Òå 1 ÊýÓò \(\mathbb{F}\) É쵀 \(n\) Ôª¶þ´ÎÆë´Îº¯Êý \[Q\left(x_1, x_2, \cdots, x_n\right)=\sum_{1 \leqslant i \leqslant j \leqslant n} a_{i j} x_i x_j \]³ÆΪ \(\mat ÔĶÁÈ«ÎÄ
posted @ 2024-06-30 09:54 Pizixsr ÔĶÁ(1) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º ±¾½Ú¸ø³ö¾À´íÂë»ù±¾²ÎÊýÖ®¼äµÄһЩÏ໥ÖÆÔ¼µÄ²»µÈʽ¹Øϵ. ¶¨Àí 1 (ººÃ÷½ç) Èç¹û´æÔÚ \(p\) Ôª¾À´íÂë, ²ÎÊýΪ \((n, K, d)\), Ôò \[p^n \geqslant K \sum_{i=0}^{\left[\frac{d-1}{2}\right]}(p-1)^i\binom{n} ÔĶÁÈ«ÎÄ
posted @ 2024-06-28 18:55 Pizixsr ÔĶÁ(1) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º ͨ¹ý 1.1 ½Ú¶Ô¾À´í½øÐеÄÖ±¹ÛÃèÊö, ÏÖÔÚ¸ø³ö¾À´íÂëµÄÈ·ÇÐÊýѧ¶¨Òå. Éè $F_p$ ÊÇ $p$ ÔªÓÐÏÞÓò. ËùÓÐÔªËØÊôÓÚ $F_p$ µÄ³¤Îª $n$ µÄÏòÁ¿ $\boldsymbol{v}=\left(v_1, \cdots, v_n\right)\left(v_i \in F_p\right) ÔĶÁÈ«ÎÄ
posted @ 2024-06-28 11:08 Pizixsr ÔĶÁ(2) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º ¾À´íÂë½éÉÜ ÒýÈë ÏÖ´úÈËÃÇÔÚÉú»îÖеÄͨÐÅ·½Ê½ÊǶàÖÖ¶àÑùµÄ,Èç´òµç»°¡¢´«Ë͵ç×ÓÓʼþÒÔ¼°ÓîÖæ·É´¬½«½ðÐÇͼƬ´«»ØµØÇòµÈ. ËäÈ»ËüÃǵÄÐÎʽ²»Í¬,µ«ÊÇËüÃǵÄÊýѧģÐÍ¿ÉÒÔa56爆大奖在线娱乐³ÉÒÔÏÂ×î¼òµ¥µÄÐÎʽ: \[\boxed{·¢·½}\overset{x}{\rightarrow}\overset{ÐŵÀ}{\cdots\cd ÔĶÁÈ«ÎÄ
posted @ 2024-06-28 00:37 Pizixsr ÔĶÁ(1) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º ´ý ÔĶÁÈ«ÎÄ
posted @ 2024-06-25 20:28 Pizixsr ÔĶÁ(2) ÆÀÂÛ(0) ÍƼö(0) ±à¼­
ÕªÒª£º 3.5 The Different Lemma 3.5.2. Let \(F^* / F\) be an algebraic extension of function fields, \(P \in \mathbb{P}_F\) and \(P^* \in \mathbb{P}_{F^*}\) w ÔĶÁÈ«ÎÄ
posted @ 2024-06-25 20:26 Pizixsr ÔĶÁ(1) ÆÀÂÛ(0) ÍƼö(0) ±à¼­